ICM 2026 — Full Schedule

International Congress of Mathematicians, Philadelphia, PA · July 22–30, 2026 · All times Eastern (local)

Wednesday, July 22, 2026

8:30 AM – 6:00 PM 121-AB Receptions & Special Events

(WM)^2 Meeting

(WM)² will take place the day before ICM 2026 and promises a vibrant day of mathematical excellence, community building, and dialogue. The program will feature invited research talks, a public lecture, a poster session, and meaningful discussions on advancing the participation and visibility of women in mathematics worldwide. This third edition of (WM)² is organized by the CWM, with the support of the ICM 2026 Local Organizing Committee and the Association for Women in Mathematics (AWM). Building on the success of previous editions in Rio de Janeiro (2018) and online (2022), the 2026 event will offer an inclusive and welcoming space for mathematical exchange and reflection. For more information, visit www.worldwomeninmaths.org.
7:00 PM – 10:00 PM Reading Terminal Market Receptions & Special Events

Welcome Reception

ICM will kick-off at Reading Terminal Market for an evening of delicious food and great entertainment. 

Access to the Welcome Reception is included with your registration.

Thursday, July 23, 2026

7:00 AM – 9:00 AM Marriott Salon G and H Receptions & Special Events

AMS Travel Support Recipient Breakfast

Through the generous support from the Alfred P. Sloan Foundation, National Science Foundation, and Simons Foundation, the American Mathematical Society has awarded travel funds enabling approximately 1,000 mathematicians and students from the United States and around the world to attend the ICM. This banquet will recognize our award recipients and partners and celebrate AMS’s role in fostering collaboration and strengthening the global mathematical community. This is an invitation-only event.

9:00 AM – 12:15 PM Terrace Ballroom Opening Ceremony

Opening Ceremony

Emceed by Brian Greene and Tracy Day, co-founders of the World Science Festival, top prizes in mathematics, including the Fields Medals, IMU Abacus Medal, Gauss Prize, Leelavati Prize and Chern Medal will be awarded at the ICM Opening Ceremony. 

12:00 PM – 1:30 PM 126-B Receptions & Special Events

Prize Winner Press Conference

12:30 PM – 1:30 PM Breaks

Lunch on Own

1:30 PM – 3:05 PM Terrace Ballroom Laudatio

Laudatios

3:45 PM – 5:20 PM Terrace Ballroom Laudatio

Laudatios

6:00 PM – 7:00 PM Terrace Ballroom Laudatio

Abacus Medal Lecture

7:30 PM – 9:30 PM Grand Hall Receptions & Special Events

Reception Honoring Jim Simons

Join us for an evening dedicated to celebrating the life of Jim Simons and his lifelong dedication to mathematical and basic scientific research, and philanthropy.

Jim Simons was an accomplished mathematician whose award-winning research revolutionized fields from condensed matter physics to topology. In 1978, he founded what would become Renaissance Technologies, a hedge fund that pioneered quantitative trading. He was an inspired and generous philanthropist, giving billions of dollars to support important work in math and science through the Simons Foundation, Simons Foundation International, Math for America and other philanthropic efforts.

Jim Simons died on May 10, 2024. Active in the foundation’s work until the end of his life, he left behind a monumental legacy.

Friday, July 24, 2026

9:00 AM – 6:00 PM Hall E - Expo Expo and Collaborations

Exhibition & Collaboration

9:00 AM – 10:00 AM Terrace Ballroom Plenary Lecture

On New Challenges in Numerical Approximation of Partial Differential Equations

Interactions with practitioners and researchers across a wide range of scientific disciplines continually pose new challenges for mathematics. Partial differential equations (PDEs) provide the fundamental language for modeling many physical phenomena, yet their mathematical analysis often remains incomplete and raises deep theoretical questions. Problems emerging from applications frequently require the development of new mathematical frameworks and, in numerical analysis, the design of novel computational methods capable of accurately approximating and simulating increasingly complex systems of PDEs. 

In this lecture, I will take the audience on a journey through some of these interdisciplinary challenges and the mathematical ideas they inspire. While many of the motivating questions originate in applications, the numerical tools and theoretical frameworks that emerge often transcend their original context, opening new challenges in numerical mathematics.

10:15 AM – 11:15 AM Terrace Ballroom Plenary Lecture

From Knots to Four-Manifolds

I will survey some connections between knot theory and four-dimensional topology. Every four-manifold can be represented in terms of a link, by a Kirby diagram. This point of view has led to progress in computing invariants of smooth four-manifolds that can detect exotic structures. I will explain how this was done in two contexts: Heegaard Floer theory and skein lasagna modules.
10:30 AM – 10:50 AM 120-AB Short Communications

A Generalization of H-Magic Labeling and Its Structural Properties

In this talk, we introduce a generalization of $H$-magic labeling, called $(F, H)$-sim-magic labeling, that is motivated by the notion of totally magic labeling. For a given graph $H$, a simple graph $G$ admits an $H$-covering if every edge in $E(G)$ belongs to a subgraph of $G$ isomorphic to $H$. An $H$-magic labeling is a bijection $f : V(G) \cup E(G) \rightarrow \{1,2,\dots, |V(G)|+|E(G)|\}$ such that for every subgraph $H'$ of $G$ isomorphic to $H$, $wt_{f}(H') = \sum_{v\in V(H')} f(v) + \sum_{e\in E(H')} f(e)$ is constant. Given two non-isomorphic graphs $F$ and $H$, let $G$ be a graph admitting both an $F$-covering and $H$-covering. In this case, the labeling $f$ of $G$ is called an $(F, H)$-sim-magic labeling if $f$ is simultaneously $F$-magic and $H$-magic. We characterize graphs admitting a $(K_2, H)$-magic labeling in terms of forbidden subgraphs when $H$ is a path, cycle, or star. Furthermore, we present constructions of $(F, H)$-sim-magic labelings for several graph operations, including join and Cartesian products. In particular, using a super edge-magic labeling of $G$, we determine a sufficient condition for the join $G+H$ to be $(K_2+H, 2K_2 + H)$-sim-magic for two connected graphs $G$ and $H$. We further construct a $(C_{2x}, C_{2y})$-sim-supermagic labeling of the Cartesian product graph $T \times K_2$ from a $(a,2)$-edge-antimagic vertex labeling of a tree $T$, for some $3 \leq x, y \leq |V(T)|-1$. This construction establishes a connection between an $\alpha$-labeling of a tree $T$ and a $(C_4, C_6)$-sim-magic labeling of the Cartesian product $T \times K_2$. These results enlarge the classes of graphs known to be $C_m$-magic for $m \geq 3$ and provide a useful tool for studying $H$-magic labeling.
10:30 AM – 10:50 AM 118-AB Short Communications

A Novel Finite Difference Scheme on Uniform Mesh for Integro-Differential Equations with Small ε-Parameters

This study presents a computational method of the first order for solving Volterra–Fredholm integro-differential equations with boundary layers. A numerical finite difference scheme is constructed on a uniform mesh. This is achieved by using the composite right-sided rectangle formula for the integral part, and interpolating quadrature rules and linear exponential basis functions for the differential part. It is demonstrated that the numerical scheme achieves first-order accuracy and uniformly converges with respect to the small ε-parameter. The efficacy of this approach is demonstrated by examining the performance of the numerical scheme in a single example.
10:30 AM – 10:50 AM 115-A Short Communications

Coalgebra Measurings and Maps Between (Co)homology Theories

The notion of a measuring coalgebra, introduced by Sweedler, induces generalized maps between algebras. This leads to an enrichment of algebras over coalgebras. In other words, the category of algebras is linearized in a manner that reminds of adding correspondences as generalized morphisms between schemes in algebraic geometry. Since an algebra may be seen as a "noncommutative scheme," we are motivated to look at morphisms between (co)homology theories induced by coalgebra measurings. In particular, we construct morphisms induced by coalgebra measurings in the following contexts:(1) Hochschild & cyclic homology of algebras(2) Chevalley-Eilenberg homology of Lie algebras(3) Operadic homology of algebras over operads(4) Cyclic cohomology of Hopf algebroids(5) Hochschild cohomology with coefficients in stable anti-Yetter Drinfeld (SAYD) modules(This is joint work with S. Kour)
10:30 AM – 10:50 AM 116-A Short Communications

Convergence of Knowledge Commons: Mutual Lessons from Mathematics and the Life Sciences

We summarize progress by the International Mathematical Knowledge Trust (IMKT) toward realizing the vision of a Global Digital Mathematics Library (GDML) and compare developments in the mathematical knowledge commons with those in the life sciences.The GDML strategic plan describes a system designed to “create a network of information that can be easily explored and manipulated” and argues that substantial portions of mathematical knowledge can become linked open data through a combination of machine-learning methods and editorial curation. The IMKT Charter articulates this vision of a mathematical knowledge commons grounded in open standards, persistent identifiers, and interoperable services.Fields like biodiversity informatics demonstrate how persistent identifiers (e.g. GBIF, Genbank, UniProt, iNaturalist) and community ontologies (e.g. Darwin Core, Gene Ontology) can enable fine-grained semantic annotation (e.g. Pensoft, Plazi, Biodiversity PMC) and integration (e.g. GloBI, TRY) across heterogeneous data sources. Similar ideas underpin medical information commons, astronomy's Virtual Observatory, chemistry's PubChem and, more generally, the FAIR (Findable, Accessible, Interoperable, Reusable) principles, where governance and standardized metadata enable interoperability among diverse data collections.A major milestone for mathematics is the transition of zbMATH to zbMATH Open, which now provides an openly accessible index of essentially the full peer-reviewed mathematical literature and research software, enriched with curated metadata, expert reviews, and links to external services such as arXiv, MathOverflow, OEIS, and DLMF. Although many entries link to full text, standardized deep linking to specific formulas, theorems, or conceptual entities remains under development. Additionally, it will be useful to link curated repositories such as LEAN’s mathlib, LMFDB, and MaRDI.Recent work on AI-based formula and concept discovery introduces semantic entities into mathematical metadata. This directly supports the GDML vision of combining automated semantic extraction with expert validation to make mathematical knowledge more navigable, interoperable, and machine-actionable. Together, these developments mark substantial progress toward a global mathematical knowledge commons.
10:30 AM – 10:50 AM 115-B Short Communications

Geometry of Anti-Poisson Involutions in the Deformations and Resolutions of Kleinian Singularities

Kleinian singularities are quotients of $\mathbb{C}^2$ by finite subgroups of $\mathrm{SL}_2(\mathbb{C})$. They are in bijection with the ADE Dynkin diagrams via the McKay correspondence. The filtered Poisson deformations of Kleinian singularities are parametrized by $\mathfrak{h}/W$, where $\mathfrak{h}$ is the Cartan space and $W$ is the Weyl group. In this talk, I will introduce certain singular Lagrangian subvarieties in the deformations and resolutions of Kleinian singularities that are related to the geometric classification of certain Harish-Chandra modules over quantizations of nilpotent orbits. The irreducible components of these singular Lagrangian subvarieties are projective lines and affine curves. I will describe how they intersect with each other through the realization of deformations of Kleinian singularities as Nakajima quiver varieties.
10:30 AM – 10:50 AM 119-AB Short Communications

Global Dynamics of a Spatially Heterogeneous Diffusive Two-Strain Epidemic Model with Varying Total Population

This work introduces an analytical approach for investigating the dynamics of diffusive two-strain epidemic models with varying total population size. First, assuming a spatially homogeneous environment, we show that the long-term dynamics of the diffusive model mirrors that of the corresponding kinetic epidemic model. In this setting, we establish that the competitive-exclusion principle holds. However, when the environment is spatially heterogeneous, the global dynamics of the diffusive epidemic model is more challenging. Under explicit and biologically meaningful assumptions on the model parameters, we establish results concerning the existence, uniqueness, and global stability of coexistence endemic equilibrium. Our findings highlight the complex interplay between population movement and spatial heterogeneity in shaping the dynamics of multi-strain infectious diseases.
10:30 AM – 10:50 AM 118-C Short Communications

Recent Results on Sampling Type Series and Applications to Image Processing

\documentclass[11pt]{article}\usepackage[utf8]{inputenc}\usepackage[T1]{fontenc}\usepackage{geometry}\geometry{margin=1in}\title{\textbf{Recent Results on Sampling Type Series and Applications to Image Processing}}\author{Tuncer Acar\\\small Selcuk University, Faculty of Science\\\small Department of Mathematics\\\small 42003, Selcuklu, Konya, T\"urkiye}\date{}\begin{document}\maketitle\begin{abstract}In this talk, we present several recent developments concerning sampling type series and their approximation properties in various function spaces. Sampling type series constitute an important class of approximation operators, playing a fundamental role in approximation theory, harmonic analysis, and signal reconstruction. In recent years, significant progress has been made in understanding their convergence behavior and rate of approximation  under different structural assumptions.A particular emphasis will be placed on the study of sampling type series in weighted function spaces. We discuss how the presence of suitable weight functions influences the approximation order, smoothness preservation, and error estimates of these operators. Connections with modulus of continuity, quantitative estimates, and embedding properties of weighted spaces will be highlighted, illustrating the advantages of working within this more general framework.In the second part of the talk, we focus on applications of sampling type series to image processing. We demonstrate how the theoretical results can be effectively employed in practical problems such as image reconstruction, denoising, and resolution enhancement. Several examples will be discussed to show how sampling based approximation schemes provide efficient and robust tools for processing digital images. The aim of this presentation is to bridge the gap between abstract approximation theory and concrete applications in image and signal processing.\end{abstract}\end{document}

10:30 AM – 10:50 AM 115-C Short Communications

Stationary Distribution of Lumpable Quasi Birth and Death Processes

This research explores extensions to the successive lumping method for Markov chains and processes, originally constrained by the requirement of entrance states. Successive lumpability enables the stationary distribution of a Markov chain to be derived by computing the stationary probabilities of a sequence of reduced chains. While the entrance state condition ensures feasibility in this approach, its strictness limits applicability. Here, we investigate methods to relax or bypass this requirement, including the construction of artificial entrance states and leveraging structural properties of specific Markov processes.
10:50 AM – 11:10 AM 118-AB Short Communications

A Second-Order Invariant-Region-Preserving Scheme for a Transport-Flow Model of Polydisperse Sedimentation

A polydisperse suspension is a mixture of a number $N$ of species of small solid particles, which may differ in size or density, dispersed in viscous fluid. The sedimentation of such a mixture gives rise to the segregation of species and flow of the mixture due to density fluctuations. In two space dimensions, and for equal-density particles, this process can be described by a hyperbolic system of $N$ nonlinear conservation laws for the particle volume fractions coupled with a version of the Stokes system for the volume-averaged flow field of the mixture. A second-order numerical scheme for this transport-flow model is formulated by combining a finite-difference approximation of the Stokes system with a finite volume (FV) scheme for the transport equations, both defined on a Cartesian grid on a rectangular domain. The FV scheme is based on a central weighted essentially non-oscillatory (CWENO) reconstruction [M. J. Castro and M. Semplice, Int. J. Numer. Methods Fluids, 89 (2019), pp. 304-325] applied to the first-order local Lax-Friedrichs (LLF) numerical flux. By the application of scaling limiters to the CWENO reconstruction polynomials (following [X. Zhang and C.-W. Shu, J. Comput. Phys., 229 (2010), pp. 3091-3120]) and utilizing that the Stokes solver generates a discretely divergence-free (DDF) velocity field, one can prove that the FV scheme has the invariant region preserving (IRP) property, i.e., the volume fractions are nonnegative and sum up at most to a set maximum value. Numerical examples illustrate the model and the scheme.
10:50 AM – 11:10 AM 119-AB Short Communications

Boundary Properties of the Newtonian Potential and Related Self-Adjoint Problems

Let $\Omega \subset {R}^n$ be an arbitrary bounded domain with smooth boundary $\partial\Omega$.Let $\varepsilon(x,y)$ be the fundamental solution of the Laplace equation$$- \Delta_x \varepsilon(x,y) = \delta(x-y),\tag{1}$$We denote the Newtonian potential by$$u_N(x) = \int_{\Omega} \varepsilon(x,y)\, f(y)\, dy.\tag{2}$$Theorem 1.For any $f \in L_2(\Omega)$, the Newtonian potential $u_N(x)$ satisfies the Poisson equation$$- \Delta_x u = f, \quad x\in \Omega,\tag{3}$$and the following boundary condition:$$-\frac{1}{2} u(x)+ \int_{\partial\Omega}\left(\frac{\partial \varepsilon(x,y)}{\partial n_y} u(y)- \varepsilon(x,y)\frac{\partial u(y)}{\partial n_y}\right)\, dS_y = 0,\quad x \in \partial\Omega.\tag{4}$$Conversely, if $u(x) \in W_2^2(\Omega)$ is a solution of the equation (3) and satisfies the boundary condition (4),then $u(x)$ coincides with the Newtonian potential defined by (2).Thus, the boundary condition (4) is the boundary condition of the classical Newtonian potential.It is known that a self-adjoint differential operator is generated by a boundary condition.The main result of this work is the followingTheorem 2. Let $L_Q$ is an invertible self-adjoint differential operator$D(L_Q)\subset W_2^2(\Omega)$, $L_Q u=-\Delta u$, satisfying at$u\in D(L_Q)$ the following boundary condition$$ Q u\big|_{\partial\Omega}=0,\tag{5}$$where $Q$ is a linear boundary operator on $\partial\Omega$, defined by theoperator $L_Q$. Then there exists an operator$V: W_2^{1/2}(\partial\Omega)\leftrightarrow L_2(\partial\Omega)$ such thatthe Green's function of the differential operator $L_Q$ is given by the formula$$ G(x,y)=\varepsilon(x,y)+\int_{\partial\Omega}V\varepsilon(x,\xi)\varepsilon(\xi,y)\, dS_\xi,\qquad (x,y)\in\Omega. \tag{6}$$
10:50 AM – 11:10 AM 115-B Short Communications

CODAS-SORT Decision Modeling Using Neutrosophic Hyper Soft Rough Matrices for Cybersecurity Applications

Cybersecurity risk assessment requires robust decision-making frameworks that can manage heterogeneous and uncertain information derived from multiple security evidence sources. In this paper, an integrated Neutrosophic Hyper Soft Rough Matrix (NHSRM) – based COmbinative Distance-based ASsessment – SORTing (CODAS-SORT) decision model is presented for effective evaluation and classification of cybersecurity threats. In the proposed approach, cybersecurity threats are evaluated using data collected from firewall alerts, intrusion detection systems, endpoint telemetry, and user behavior analytics. Lower and upper neutrosophic evaluations are combined to obtain a crisp decision matrix, which is subsequently examined using the CODAS technique. Euclidean and Taxicab distances from the negative ideal solution are employed to derive assessment scores, which are further categorized into predefined cybersecurity risk classes through the CODAS-SORT mechanism. The complete decision model is implemented using MATLAB, ensuring computational transparency, reproducibility, and practical feasibility. A representative cybersecurity case study is presented to demonstrate the applicability and effectiveness of the proposed framework, producing coherent and interpretable risk classification results.
10:50 AM – 11:10 AM 118-C Short Communications

Global Hypoellipticity for Systems on Asymptotically Euclidean Manifolds

We study the global hypoellipticity of the operator \[ \mathbb{L} = \mathrm{d}_t + \sum_{k=1}^m \omega_k \wedge \partial_{x_k},\]defined on differential forms over product manifolds \(M \times \mathbb{T}^m\). Explicitely, \(M\) is a non-compact manifold, diffeomorphic to the interior of an asymptotically Euclidean manifold, that is, a compact manifold with boundary, equipped with a scattering metric, while \(\mathbb{T}^m\) is the \(m\)-dimensional torus. In the expression of \(\mathbb{L}\), \(\mathrm{d}_t\) denotes the exterior derivative acting on the variable \(t\) on \(M\), \(\omega_1,\dots,\omega_m\) are smooth, real-valued, closed \(1\)-forms on \(M\), and \(x = (x_1, . . . , x_m )\) are the angular coordinates on \(\mathbb{T}^m\). Operators of the form \( \mathbb{L} \) arise naturally in the context of involutive structures, where the associated distribution is closed under the Lie bracket. Locally, they can be interpreted as systems of commuting first-order partial differential equations, with a geometric structure encoded by the \(1\)-forms \(\omega_k\) , \(k = 1, . . . , m\). Extending known results in the compact setting, we characterize the global hypoellipticity of \(\mathbb{L}\) in terms of arithmetic properties of the forms \(\omega_k\), \(k=1,\dots,m\). The analysis relies on microlocal techniques and a version of the Hodge Theorem available on asymptotically Euclidean manifolds. This is joint work with A. Kirilov, W. A. A. de Moraes, and P. M. Tokoro (Universidade Federal do Paraná, Curitiba, Paraná, Brazil), published inThe Journal of Geometric Analysis.
10:50 AM – 11:10 AM 115-A Short Communications

Maxmin-$\omega$ Systems: The Generalization of Max-Plus and Min-Plus Systems

Maxmin-$\omega$ systems are introduced as a parametric generalization that bridges max-plus and min-plus algebraic systems through a threshold $0<\omega\leq 1$. When $\omega=1$, the system behaves as a classical max-plus system; when $\omega\approx 0$, it corresponds to a min-plus system; and for intermediate values of $\omega$, the system exhibits a fuzzified interaction between maximization and minimization. Interestingly, several fundamental properties that hold in pure max-plus or min-plus systems no longer hold in the maxmin-$\omega$ setting. This breakdown reveals a richer, more flexible system that enables the modeling of nonlinear transitions between optimization extremes. We further discuss how these altered properties influence solution methods for problems such as linear equations and eigenproblems, providing insights into the behavior and potential applications of this new class of systems.
10:50 AM – 11:10 AM 116-A Short Communications

Multi-Headed Transformer Architectures as Time-Dependent Wasserstein Gradient Flows

In recent years, transformer architectures have revolutionized the field of language processing, opening the door to previously unforeseen possibilities. However, from a theoretical point of view, the mathematical models proposed in the literature often lack direct contact with the actual architectures and depend on strong simplifying assumptions. In this paper, we reduce this gap by modelling the data flow in multi-headed transformer architectures as time-dependent gradient flows for a suitable interaction energy capturing the design of the attention mechanism. The explicit dependence on time allows us to consider different weights for each head and for each layer, without imposing constraints on the initialization method. Moreover, we prove that the $\omega$-limit of the gradient flows are stationary points of the interaction energy functional. Finally, we analyse the stability of the gradient flows considering perturbations of both the initial data and the weights. Specifically, on the one hand, we study the robustness of the proposed models with respect to noisy inputs, establishing a continuous dependence of the gradient flows on the initial data and uniqueness of the flows. On the other hand, we prove the $\Gamma$-convergence of the perturbed interaction energy to the unperturbed one, leading to the convergence of the corresponding gradient flows.
10:50 AM – 11:10 AM 115-C Short Communications

Traffic Dynamics and Control in Conserved Fractal Network

In an urban-scale traffic system, traffic networks are formed in a city as it comprises roads and intersections defining the connectivity between them. Road networks play a crucial role in connecting urban centers and improving the connectivity of isolated areas where transportation is unavailable. Despite the complexity of modeling traffic flow on a network in recent years, many different robust and influential theories have been presented in the last decade. The urban road transportation system is investigated at the network level with the help of a macroscopic fundamental diagram (MFD). Utilizing the conventional macroscopic model, the MFDs were obtained successfully for low density, but it failed to predict the traffic behavior at high densities due to traffic instabilities. To overcome this issue, a simplified speed-matching model has been proposed where the MFD has been reproduced for all density ranges.In real traffic dynamics, traffic control serves as an indispensable component in optimizing the traffic flow, especially on networks. To analyze the varied complexity of traffic dynamics, the percolation back bone fractal network is characterized via cell-transmission model. Considering a generalized flow-density relation, dynamic model is modified to scrutinize the impact of transition rates on traffic flow in a conserved network. The macroscopic fundamental diagrams attained through numerical simulation are investigated for homogeneous as well as heterogeneous transition rates. For first-generation fractal network, unimodal or bimodal traffic currents are observed with respect to mean density. Further, for second-generation fractal network, two types of density waves are observed depending upon the number of vehicles present in system: uniform equilibrium state and oscillatory state. It is observed that the transition rates corresponding to singly-connected nodes can control the traffic dynamics to ensure a uniform stationary flow, which cannot be achieved via the doubly-connected and quadruple connected nodes.
11:10 AM – 11:30 AM 119-AB Short Communications

A Safety-Oriented Mathematical Model of Autonomous Vehicle Adoption for Blind and Visually Impaired Individuals

This study advances safety research and human behavior analytics by developing a mathematical framework to analyze autonomous vehicle (AV) adoption and use among blind and visually impaired individuals, for whom AV systems represent a safety-critical mobility interface rather than a mere assistive convenience. We model AV adoption as a coupled socio-technical system in which trust, behavioral adaptation, and non-visual human–AI interaction directly influence safety outcomes. Using a system of nonlinear differential equations, we incorporate behavioral variables that capture reliance on auditory and haptic feedback, perceived system reliability, and risk sensitivity under visual impairment. Control parameters represent accessibility-focused safety policies, inclusive interface design, and targeted public awareness interventions. Existence, uniqueness, and stability analyses characterize conditions under which AV adoption remains behaviorally stable and safety-resilient for blind users. Sensitivity analysis using Latin Hypercube Sampling and Partial Rank Correlation Coefficients identifies dominant behavioral and policy drivers of safe adoption. Our findings indicate that accessibility-centered safety interventions significantly improve trust calibration and reduce unsafe behavioral responses during periods of system uncertainty or failure. The results highlight the necessity of integrating disability-specific human behavior analytics into autonomous vehicle safety modeling, policy design, and ethical AI deployment. This work positions accessibility for blind and visually impaired individuals as a foundational component of equitable and inclusive transportation safety research.
11:10 AM – 11:30 AM 118-AB Short Communications

Average Kernel Sizes - Computable Sharp Accuracy Bounds for Inverse Problems

The reconstruction of an unknown quantity from noisy measurements is a mathematical problem relevant in most applied sciences, for example, in medical imaging, radar inverse scattering, or astronomy. This underlying mathematical problem is often an ill-posed (non-linear) reconstruction problem, referred to as an ill-posed inverse problem. To tackle such problems, there exist a myriad of methods to design approximate inverse maps, ranging from optimization-based approaches, such as compressed sensing, over Bayesian approaches, to data-driven techniques such as deep learning. For all stable approximate inverse maps, there are accuracy limits that are strictly larger than zero for ill-posed inverse problems, due to the accuracy-stability tradeoff [Gottschling et al., SIAM Review, 67.1 (2025)] and [Colbrook et al., Proceedings of the National Academy of Sciences, 119.12 (2022)]. The variety of methods that aim to solve such problems begs for a unifying approach to help scientists choose the approximate inverse map that obtains this theoretical optimum. Up to now there do not exist computable accuracy bounds to this optimum that are applicable to all inverse problems. We provide computable sharp accuracy bounds to the reconstruction error of solution methods to inverse problems. The bounds are method-independent and purely depend on the dataset of signals, the forward model of the inverse problem, and the noise model. To facilitate the use in scientific applications, we provide an algorithmic framework and an accompanying software library to compute these accuracy bounds. We demonstrate the validity of the algorithms on two inverse problems from different domains: fluorescence localization microscopy and super-resolution of multi-spectral satellite data. Computing the accuracy bounds for a problem before solving it, enables a fundamental shift towards optimizing datasets and forward models.
11:10 AM – 11:30 AM 115-B Short Communications

Continuity of Coordinate Functionals for Ideal Schauder Bases

Schauder bases, introduced by Juliusz Schauder in the 1920s, became a central tool in the study of separable Banach spaces, providing series representations of their elements. For many years it was conjectured that every separable Banach space admits a Schauder basis. This belief was overturned by Enflo’s breakthrough in 1973, when he constructed a separable Banach space without any Schauder basis. Enflo’s example stimulated the search for weaker or more flexible notions of basis capable of accommodating the full class of separable Banach spaces. Various generalizations have since been proposed, including frames, Markushevich bases, and finite-dimensional decompositions. In this context, ideal Schauder bases provide a framework in which convergence is governed by ideals on naturals, offering a setting to investigate how classical basis phenomena may extend beyond the traditional notion. This line of research reflects the broader effort to reconcile representation theory with the intrinsic diversity of separable Banach spaces.An open problem in the theory of ideal Schauder bases has been whether the associated coordinate projections must be continuous. Unlike the classical setting, where boundedness of projections follows from standard functional-analytic arguments, these methods break down in the ideal framework and leave the question unresolved. In this talk, I will explain the source of these difficulties, show why classical techniques cannot be directly adapted, and present a solution that establishes continuity under appropriate assumptions. This work answers a question of Vladimir Kadets and was obtained jointly with Tomasz Kania and Noe de Rancourt.
11:10 AM – 11:30 AM 118-C Short Communications

Hypergeometric Matrix Functions and Their Properties

In this talk, a generalization of the extended gamma matrix function(EGMF) and extended beta matrix function(EBMF) are to be introduced using the four-parameter Mittag-Leffler matrix function. Several fundamental properties will be explored. Further, extended hypergeometric matrix function(EHGMF) and extended confluent hypergeometric matrix function(ECHGMF) will be investigated by utilizing the newly generalized extended beta function. Various properties of these functions are examined, such as their integral representations, differentiation formulas, transformation formulas, beta transforms, recurrence relations and generating functions.
11:10 AM – 11:30 AM 115-C Short Communications

Lessons on the Icosahedron

Through lessons on the icosahedron, we aim to address three key questions of teaching: What? For whom? How? We seek answers that lie somewhere between the big ideas of renowned mathematics educators, which have not yet been fully integrated into teaching practice, and experiences from contemporary classrooms, which often fall outside established theoretical frameworks. These answers are summarized as concise didactic principles and illustrated through exercises for mathematics students in an undergraduate course on the methodology of teaching mathematics.The first principle -- the principle of minimality -- is illustrated through a description of a workshop conducted by students with pupils aged 14. The workshop task was to estimate the minimal edge length of an icosahedral box that can hold 0.5 kilograms of sugar (using cardboard, geometric tools, scissors, glue, kitchen scales, and a packet of sugar). This principle aligns with the Moore model of learning and the Feynman model of simplicity.The second principle -- the principle of adaptation -- is illustrated through an analysis of the students’ work in which they were tasked with preparing three lectures on the same topic: a school-level lecture, a popular lecture, and an academic lecture. The topics they could choose from included the truncated icosahedron, the Dymaxion (Fuller’s) world map, the tensegrity icosahedron, the great icosahedron. The principle follows the sociocultural approach, based on the ideas of Vygotsky, which emphasizes the importance of social interaction and the context in which learning occurs. The third principle -- the principle of activity -- is illustrated by the task of examining the symmetry group of the icosahedron using both concrete and abstract models. Students were seeking the most effective ways of learning group theory and studying Klein’s famous Lectures on the Icosahedron, in the spirit of the ideas of Pólya, Skemp and others.
11:10 AM – 11:30 AM 116-A Short Communications

On the E-Base of Finite Lattices: Semidistributive, Modular, and Geometric Lattices

Implicational bases (IBs) are a well-known representation of finite closure spaces and their closure lattices. Implications go by many names in a broad range of fields, e.g., attribute implications in Formal Concept Analysis, functional dependencies in database theory, or Horn clauses in propositional logic.In lattice theory, implications translate into join covers, i.e., sets of relations $j\leq j_1\vee \dots \vee j_k$, $k\geq 1$, on the set of join-irreducible elements of a lattice.The representation by an IBis not unique, and a closure space usually admits multiple IBs.Among these, the canonical base, the canonical direct base as well as the $D$-base aroused significant attention due to their structural and algorithmic properties.The study of free lattices was influential in bringing up an IBof a new sort, which was called the $E$-base.It is a refinement of the $D$-base that, unlike the aforementioned IBs, does not always accurately represent its associated closure space.This leads to an intriguing question: for which classes of (closure) lattices do closure spaces have a valid $E$-base?Finite lower bounded lattices are known to form such a class.In recent publication \url{https://arxiv.org/abs/2502.04146},we prove that for semidistributive lattices, the $E$-base is both valid and minimum.Among other results, we look into $E$-base in a few classes of closures spaces with the Exchange Axiom and we characterize those modular and geometric lattices that have valid $E$-base.Finally, we prove that any lattice is a sublattice of a lattice with valid $E$-base.
11:10 AM – 11:30 AM 115-A Short Communications

Projectives Over Leavitt Path Algebras

The monoid of isomorphism classes of finitely generated projective modules is a fundamental invariant of a Leavitt path algebra, it allows us to explore the relation between its algebraic structure and the combinatorics of the underlying graph. This monoid underlies the Grothendieck group $K_0$ via group completion and plays a central role in classification problems, Morita equivalence, and algebraic $K$-theory.In this talk, we study this monoid across several generalizations of Leavitt path algebras. We begin with weighted Leavitt path algebras, examining how edge weights modify the defining relations of the aforementioned monoid, with particular attention to the confluence and cancellation properties of the monoid. Next, we consider the monoid of finitely generated graded projective modules, where the grading provides a refinement of its ungraded version. Here, we focus on the standard grading when investigating the corresponding monoid. (joint work in progress with A. Sebandal). Finally, we discuss Leavitt path algebras of quantum quivers, introduced in our joint work with J. Graham and J. Palin. We describe the monoid of iso-classes of finitely generated projective modules in this setting and comment on its $K_0$-group. These algebras are particularly interesting as they provide a machinery to explore Leavitt path algebras in the context of quantum graphs introduced by Brannan et al.
11:10 AM – 11:30 AM 120-AB Short Communications

Structural Study of Refractory Compound

Structural Study of Refractory CompoundPurvee BhardwajJNCT Professional University, Bhopal-462038, (MP) IndiaEmail: purveebhardwaj@gmail.compurvee.bhardwaj@jnctpu.edu.inAbstractIn this work, we have systematically examined high-pressure structural phase transition behavior of the refractory compound Curium Sulfide (CmS). In order to provide a more accurate representation of interatomic forces under compression, an Extended Interaction Potential (EIP) model has been developed that incorporates the zero-point energy effect along with a three-body interaction potential framework. According to the research, a first-order structural transformation is indicated by the phase transition pressure, which is characterized by a dramatic collapse in volume. The theoretical and experimental patterns found in comparable refractory compound are satisfactorily aligned with the predicted transition pressures and related volume collapses. Additionally, the study provides important information about the mechanical stability and stiffness of the compound under various pressure regimes by reporting the elastic constants, their combinations, and pressure derivatives. To clarify the nature of bonding and lattice compressibility in CmS, the pressure dependence of elastic constants, bulk modulus, and shear modulus has been examined and addressed. The current work contributes to the larger study of actinide compounds under extreme conditions by offering a thorough theoretical framework for comprehending the structural, elastic, and thermo-physical properties of the transuranic refractory compound CmS.Key words: High pressure, Crystal structure, Elastic properties, Phase transition. Classification: 06B05: Structure theory, 74E15: Crystalline structure
11:30 AM – 11:50 AM 115-A Short Communications

Characterization of Rubik’s Cube Groups Using Fractal Structure

We present a new approach to characterize the well-known Rubik’s cube group by using the fractal nature of the cube. We use this characterization to count the possible configurations of both the 2×2×2 and 3×3×3 cubes.
11:30 AM – 11:50 AM 120-AB Short Communications

Conservation Laws for Einstein Equations with a Cosmological Constant

In this work, we consider Lorentzian spacetimes whose Ricci curvature is proportional to the metric. We formulate a Hamiltonian initial value problem for Lorentzian Einstein manifolds with a spacelike rotational isometry. We establish various conservation laws for these manifolds in the sense that we show the existence of various spacetime divergence-free vector field densities. The central conservation law corresponds to a Hamiltonian energy of the system. Subsequently, we also construct such divergence-free vector field densities corresponding to the symmetries of internal structure of the dimensionally reduced field equations. This work is relevant to study the asymptotics and stability properties of these spacetimes. The motivation for expressing the conservation laws in the form of spacetime divergence-free vector field densities is that it is particularly convenient to express balance-laws near asymptotic null infinity.
11:30 AM – 11:50 AM 118-AB Short Communications

Constructive Analysis of Boundary Value Problems for Nonlinear Integro-Differential Equations

This study focuses on a family of nonlinear two-point boundary value problems (BVPs) for systems of integro-differential equations: \[\begin{equation}\label{eq1} \frac{\partial V}{\partial t}=f\left(x,t, \psi(t)+ \int \limits_{0}^{x}V(\xi,t)d \xi,V \right), \quad V \in \mathbb{R}^{n}, \quad (x,t) \in\Omega,\end{equation}\]\[\begin{equation}\label{eq2} g\left(x,V(x,0),V(x,T)\right)=0, \quad x \in [0,\omega],\end{equation}\]where $\Omega = [0,\omega]\times (0,T)$, the functions $f:[0,\omega]\times [0,T]\times \mathbb{R}^{2n} \to \mathbb{R}^{n}$ and $g:[0,\omega ]\times \mathbb{R}^{n} \times \mathbb{R}^{n} \to \mathbb{R}^{n} $ are continuous.We propose a constructive algorithm for finding solutions based on a modified version of D.S. Dzhumabaev’s parametrization method. The approach involves partitioning the time interval and introducing additional parameters as the values of the desired solution at the nodes of the partition, effectively reducing the original problem to an equivalent family of multipoint BVPs.Conditions for the feasibility and convergence of the proposed algorithm are established. These conditions also serve as sufficient conditions for the existence of an isolated solution within a specified neighborhood. A key feature of the study is its application to a class of nonlinear hyperbolic equations with mixed derivatives and nonlocal boundary conditions.
11:30 AM – 11:50 AM 115-B Short Communications

Drawing Infinite Graphs

The classical Rado graph (or random graph) occupies a central place in model theory, Fraïssé theory, and combinatorics: it is the unique countable graph that appears with probability one when each pair of natural numbers is independently connected with probability 1/2. Its uniqueness was proved by Erdős and Rényi, prompting Erdős and Spencer to remark that “the theory of infinite random graphs is demolished by Erdős and Rényi’s theorem.” Yet this construction relies on repeatedly tossing the same (possibly asymmetric) coin. Our goal is to revive the study of infinite random graphs generated instead by a sequence of different asymmetric coins. This broader framework allows us to explore how far one may deviate from the classical Rado graph while still obtaining a well-defined “almost sure” infinite structure. The aim of the lecture is to present the central ideas without unnecessary technicalities, highlighting how randomness, structural invariance interact to produce a surprisingly rich landscape of infinite random graphs, especially with regard to questions about which graphs can be drawn. The results are joint with Jarosław Swaczyna, Ziemowit Kostana, and Leonardo N. Coregliano.
11:30 AM – 11:50 AM 115-C Short Communications

FUNDAPROMAT: Spreading the Joy of Mathematics

The Panamanian Foundation for the Promotion of Mathematics (FUNDAPROMAT) is a private non-profit Foundation based in the Republic of Panama whose mission is to change the world's perception so that one and all can experience mathematics as accessible, relevant and inherently joyous. So far the Foundation has organized more than 700 free math outreach events, both virtual and in-person, with more than 70,000 participants, including Panamanians and internationals from all over the world. In this short presentation, Dr. Shakalli will briefly describe what we do in FUNDAPROMAT, how we do it and why we do it. Dr. Shakalli will also share the teaching resources that students, teachers and parents can download for free on the FUNDAPROMAT website https://www.fundapromat.org/en.
11:30 AM – 11:50 AM 119-AB Short Communications

Finite-Dimensional Approximations of Push-Forwards on Locally Analytic Functionals

We develop a functional-analytic framework for approximating the push-forward induced by an analytic map from finitely many samples. Instead of working directly with the map, we study the push-forward on the space of locally analytic functionals and identify it, via the Fourier--Borel transform, with an operator on the space of entire functions of exponential type. This yields finite-dimensional approximations of the push-forward together with explicit error bounds expressed in terms of the smallest eigenvalues of certain Hankel moment matrices. Moreover, we obtain sample complexity bounds for the approximation from i.i.d. sampled data. As a consequence, we show that linear algebraic operations on the finite-dimensional approximations can be used to reconstruct analytic vector fields from discrete trajectory data. In particular, we prove convergence of a data-driven method for recovering the vector field of an ordinary differential equation from finite-time flow map data under fairly general conditions.
11:30 AM – 12:30 PM Terrace Ballroom Plenary Lecture

Local and Global Langlands Conjecture(s) Over Function Fields

We will describe a set of conjectures whose common motif is that a classical statement is obtained from its geometric counterpart by the procedure of (categorical) trace of Frobenius. 

11:30 AM – 11:50 AM 118-C Short Communications

On Density and Dentability in Norm-Attainable Classes

Characterizations of properties of operators between Banach spaces have been developed over decades. However, the density and dentability of operators, as well as their relationship, have not been characterized in norm-attainable classes. The main objective of this work has been to characterize both density and dentability in norm-attainable classes. Specifically, the objectives were to characterize density in norm-attainable classes, to characterize dentability in norm-attainable classes, and to establish the relationship between density and dentability in these classes. The methodology employed fundamental results such as the Hahn-Banach and Radon-Nikodým theorems, in addition to technical and geometric properties. We have proved that a countable union of dense norm-attainable subclasses of \( B(H) \) is dense in \( B(H) \). Moreover, we have shown that a finite intersection of dentable norm-attainable classes is dentable and that a dense norm-attainable class is necessarily dentable. This study is significant in mathematical analysis and mathematics at large, particularly in relation to optimization problems and algorithmic concentration in sphere packing. Beyond mathematics, these concepts find applications in population studies. For instance, density analysis helps distinguish between densely and sparsely populated areas, while dentability can reveal linear or nonlinear settlement patterns based on separability conditions. Additionally, density plays a crucial role in the study of stars and the universe, offering insights into various astrophysical processes and the structure of the cosmos. The open problems presented offer opportunities for further research.
11:30 AM – 11:50 AM 116-A Short Communications

Towards Computing Canonical Lifts of Ordinary Elliptic Curves in Medium Characteristic

Let $E/F_q$ be an elliptic curve over a finite field. Schoof's method \cite{schoof1985elliptic} gives a polynomial time algorithm to count thenumber of points of $E$. The complexity was later improved by Atkin and Elkies to give the SEA algorithm. %\cite{elkies1992explicit, elkies1998, bmss}.The algorithm can be seen as an incarnation of $\ell$-adic \'etalecohomology: if $\chi(t)$ is the characteristic polynomial of the Frobenius$\pi_q$, $\chi(t) \mod \ell$ is computed modulo several primes $\ell$ by looking at the action of $\pi_q$ on (a subgroup of) the $\ell$-torsion$E[\ell]$. The CRT algorithm allows to reconstruct $\chi(t)$ once we have enough precision (as bounded by the Hasse-Weil bound).One can compute~$\chi\mod{\ell}$~ in ~$\tilde{O}\left((\ell+\log{q})\ell\log{q}\right)$, hencereconstruct $\chi$ in $\tilde{O}\left(\log^4 q)\right)$.In 2000, a second class of algorithms was introduced by Satoh \cite{satoh2000canonical}, using the Lubin-Serre-Tate Theorem. $\mathcal{E}/F_q$ (with $q=p^n$) be an ordinary abelian variety. A classical result due to Lubin, Serre and Tate Let $q=p^n$, let $Z_q$ be the ring of Witt vectors of $F_q$, and $Q_q=\mathrm{Frac}(Z_q)$the unique unramified extension of $Q_p$ of degree~$n$.Then \cite{LST} establishes the existence of a unique (up to isomorphisms) elliptic curve $E^{\uparrow}$ over $Z_q$ for every ordinary elliptic curves $E/F_q$ such that the modulo $p$ reduction of $E^{\uparrow}$ is $E$ and $\mathrm{End}(E^{\uparrow})\cong End(E)$ as a ring. The curve $E^{\uparrow}$ is called the \emph{canonical lift of $E$}. Then the trace of the Frobenius morphism is deduced using \emph{crystalline cohomology}. Let $p$ be a prime; using modular polynomial $\Phi_p$, Satoh et al \cite{satoh2000canonical,vercau,gaudrySurveyComptage} developed several algorithms to compute the canonical lift of an ordinary ellipticcurve $E$ over $F_{p^n}$ with $j$-invariant not in $F_{p^2}$.When $p$ is constant, the best variant has complexity$\tilde{O}(n m)$ bit operations to lift $E$ to $p$-adic precision~$m$.As an application, lifting $E$ to precision $m=O(n)$ allows torecover its cardinality in time $\tilde{O}(n^2)$.However, taking $p$ into account the complexity is$\tilde{O}(p^2 n m)$, so Satoh's algorithm can only be appliedto small~$p$.We are interested in the dependency of $p$ of the algorithm. We will now assume that $p>2$ for simplicity. The modular polyn
11:50 AM – 12:10 PM 115-C Short Communications

Expressions of Factorisation in Japan During the Edo Period

There were several schools of mathematics in Japan during the Edo period (1603 - 1868). The most famous and popular school was the Seki school [関流] of the renowned mathematician Seki Takakazu [関孝和] (?-1708). In addition to the Seki school, there were various other schools such as Takuma school [宅間流], Shisei-Sanka school [至誠賛化流], Saijyo school [最上流] etc. 　　And the mathematical books were written in different expressions in different schools. The Seki school's way of expressing mathematics is inspired by the motif of Sangi [算木], which was introduced from China to Japan. Takuma school does not use Sangi expressions of arithmetic sticks. Negative numbers are written as fu (フ) in Japanese katakana [カタカナ], and numbers are one(一), two(二), three(三) in Japanese kanji [漢字]. 　　We shall examine a book dealing with mathematical expressions at Takuma School, specifically concerning factorisation. It is not known how factorisation was written in Japanese mathematics during the Edo period. Regarding how factorisation was written in vertical-writing mathematics. We read all five volumes of Oka's “Kijutsu Kairohō [起術解路法] (Takuma School’s Collection of Method of Resolving the Path of Techniques)”. Volumes 4 and 5 of this book cover factorisation. “Kijutsu Kairohō” volumes 4 presents all problems using plane figures, yet factorisation is employed to solve every single one. Some expressions are highly complex and are presented without ( ) expression.　　When students solved an excellent mathematical problem, they thanked the gods or Buddha, wrote the problem and the formula for solving it on a wooden panel called sangaku[算額] (votive mathematical tablets), and dedicated it to a shrine or a temple. In the Edo period, shrines and temples were the most crowded places, not only for festivals, celebrations, and funerals, so by displaying sangaku there, students could show many people the problems that could be solved. 　　The Sangaku at Takuma School in Zenkoji Temple[善光寺] features a problem requiring factorisation to solve. This problem was highly complex, and presenting it to the public at the renowned temple served as a form of publicity for the Takuma School and its affiliated student. I am interested in mathematical schools other than the Seki school. I will also focus on the spread of the school's students in Japan.
11:50 AM – 12:10 PM 118-C Short Communications

Fractional Calculus of Zeta Functions: Further Results

In this short communication, we deal with new analytic results concerning fractional calculus of zeta functions. First, we study the zero-free regions of the $\alpha$-order fractional derivative of the Riemann zeta function. In particular, we show some zero-free regions of $\zeta^{(\alpha)}(s)$. Furthermore, we prove existence of a zero-free region in the left half-plane depending on the complement of a circle of finite radius $r_{\alpha}$ centered at the origin. In the second part, we prove and discuss the property of universality of $\zeta^{(\alpha)}(s)$. As a consequence, a wide class of analytic functions can be approximated by shifts of $\zeta^{(\alpha)}(s + i \tau)$, $\tau \in \mathbb{R}$.
11:50 AM – 12:10 PM 119-AB Short Communications

Hyperbolic Periodic Orbits in Four Dimensional Systems Detected via Averaging Theory

By making suitable choices for the first integrals, we revisit the four-dimensional system given by [1], presenting a simplified proof of its main result concerning the number of limit cycles and extending its validity to a larger domain. Moreover, we extend this analysis to a wider class of perturbations by applying first and second-order averaging theory.[1] Llibre, J., Teixeira, M. A.: Limit cycles for a mechanical system coming from the perturbation of a four–dimensional linear center. Journal of Dynamics and Differential Equations, 18(4), 931–941 (2006).[2] Gonçalves, L. F., Garcia, R. A.: Hyperbolic periodic orbits in four dimensional systems detected via Averaging Theory. Submitted to Journal of Differential Equations (2025).
11:50 AM – 12:10 PM 120-AB Short Communications

Numerical Modeling of Wave Attenuation by Hybrid Green–Grey Coastal Infrastructure

Hybrid coastal infrastructure that integrates engineered structures with nature-based solutions has emerged as a promising approach to reducing wave impacts while enhancing coastal resilience and ecosystem sustainability. This study investigates wave attenuation mechanisms in hybrid systems composed of conventional coastal structures, such as submerged breakwaters, piles, or fences, combined with coastal vegetation, including mangroves and seagrass, with a particular focus on tsunami-like long waves representative of the Aceh event. An analytical wave transmission coefficient is derived to quantify wave attenuation induced by the hybrid infrastructure. The governing shallow water equations are then solved numerically to capture wave propagation, transmission, and energy dissipation across hybrid configurations under varying hydrodynamic and geometric conditions. Model performance is validated against available experimental data, with emphasis on wave transformation characteristics relevant to the Aceh tsunami case. The numerical results demonstrate that hybrid configurations provide significantly stronger wave attenuation than single-component defenses, with vegetation contributing additional damping through drag-induced momentum loss and enhanced energy dissipation. Parametric analyses indicate that wave reduction is governed by the submergence, dimensions, and physical characteristics of the vegetation. These findings highlight the synergistic effects of hybrid coastal infrastructure in reducing wave height, transmission coefficients, and nearshore hydrodynamic energy, providing a quantitative basis for the design of adaptive, cost-effective, and environmentally sustainable coastal protection strategies for sediment-rich and low-lying coastlines exposed to increasing tsunami and climate-driven hazards.
11:50 AM – 12:10 PM 115-A Short Communications

On Nil Ideals of Leavitt Path Algebras Over Commutative Rings

In this talk we show that for any graph $E$ and for a commutative unital ring $R$, the nil ideals of the Leavitt path algebra $L_R(E)$ depend solely on the nil ideals of the ring $R$. We also obtain results on the Jacobson radical of $L_R(E)$ for a graph $E$ with no regular vertex. Additionally, we obtain that for a nil ideal $I$ of a Leavitt path algebra $L_{R}(E)$, the ideal $M_2(I)$ is also nil thus establishing that Leavitt path algebras over arbitrary graphs satisfy the K$\ddot{o}$ethe's conjecture.
11:50 AM – 12:10 PM 116-A Short Communications

Permutation Resemblance

Constructing bijection maps with strong resistance against differential attacks has been an important problem in cryptanalysis. More precisely, given a polynomial $f\in\mathbb{F}_q[x]$, the differential uniformity of $f$, $\delta_f$, is defined by the maximum number of solutions in $\mathbb{F}_q$ to the equation $f(x+a)-f(x)=b$, where $(a,b)$ run through all elements of $\mathbb{F}_q^{*}\times \mathbb{F}_q$. The lower the value of $\delta_f$, the more resistant $f$ is to differential attacks when used as an S-box. Functions with the optimal differential uniformity are called almost perfect nonlinear (APN) over $\mathbb{F}_{2^e}$ (where $\delta_f=2$), and are called planar over finite fields of odd characteristics (where $\delta_f=1$). It is desirable that $f\in\mathbb{F}_q[x]$ not only has low differential uniformity but is also a permutation polynomial over $\mathbb{F}_q$, which means that the evaluation map $x\mapsto f(x)$ is a bijection. In general, such optimal functions are rare. For example, the existence of APN permutations over $\mathbb{F}_{2^e}$ for even $e\ge 8$ has remained open since 2010, following the celebrated discovery of the only known class of APN permutations over $\mathbb{F}_{2^6}$ by Browning et al. Motivated by the problem of constructing permutation polynomials with low differential uniformity, we introduce the notion of permutation resemblance, which measures the distance of a function from being a bijection. For a function $x\mapsto f(x)$ over a finite group $(\mathcal{G},+)$, the permutation resemblance of $f$, P-Res$(f)$, is defined by the minimum cardinality of the image set of $f-h$, where $h$ runs through all bijection maps over $\mathcal{G}$. In this talk, we present our recent results on permutation resemblance. In particular, we formulate an integer program that computes P-Res$(f)$, and rephrase the problem of finding a permutation polynomial with the lowest differential uniformity into an integer program. Moreover, we show that we can significantly reduce the problem size of the latter, while compromising the optimality, by computing the P-Res$(f)$ first.
11:50 AM – 12:10 PM 115-B Short Communications

Recent Fixed Point Results on Digital Metric Spaces

The 21st century is widely regarded as the age of information and technology, in which fixed point theory plays a crucial role in image processing and computer graphics. One of the main objectives in this area is to obtain meaningful fixed point results on digital images. In recent years, digital topology has become an active research field, providing a solid mathematical framework for the analysis of digital images. In this talk, we introduce a class of F-contractions in digital metric spaces and establish fixed point theorems via F-contractive mappings. Moreover, we present an application of the Banach fixed point theorem to digital images.
11:50 AM – 12:10 PM 118-AB Short Communications

Tseng's Type Methods in Continuous and Discrete Time for Quasi-Variational Inequalities

Quasi-variational inequalities are a significant extension of classical variational inequalities, where the constraint set depends on the solution itself. They were initially introduced by Bensoussan et al. in 1973 in the context of impulse control problems and have since evolved into powerful mathematical tools with applications in economics, engineering, operations research, and partial differential equations.This talk presents an approach for obtaining approximate solutions to quasi-variational inequalities in a real Hilbert space by modifying Tseng's scheme, which was originally designed for variational inequalities. The study explores the existence of equilibrium points and investigates convergence results related to dynamical systems. Linear convergence for discretized systems is examined through examples, illustrations, and special cases.
12:00 PM – 1:30 PM 120-C Receptions & Special Events

LGBTQ+ and Allies Lunch

Spectra, the Association for LGBTQ+ Mathematicians, is hosting its first ever ICM reception for LGBTQ+ mathematicians and our allies. We're welcoming folks from all backgrounds to join us in this intimate social setting to meet and socialize. Starting from an informal set of concerned mathematicians in the 90s, Spectra has grown into an international organization advocating for the professional development and well-being of its members. We're excited to host our first official ICM event and hope that you will join us.

12:00 PM – 6:00 PM Hall E - Expo Poster Presentations

Poster Exhibition

"Heat Regulation Model in the Human Body During Cycling due to the Met-Abolic Effect" by Saraswati Acharya (15 - Numerical Analysis and Scientific Computing)

"Preconditioned Iterative Methods and Sensitivity Analysis for a Class of Saddle Point Problems" by Sk Safique Ahmad (15 - Numerical Analysis and Scientific Computing)

"Lambda admissible subspaces of self adjoint matrices" by Francisco Arrieta Zuccalli (15 - Numerical Analysis and Scientific Computing)

"Efficient Numerical Implementation of a Stochastic Time-Fractional Coupled Flow Model" by Abdumauvlen Berdyshev (15 - Numerical Analysis and Scientific Computing)

"A Poisson-Nernst-Planck Single Ion Channel Model and its Effective Finite Element Solver" by Zhen Chao (15 - Numerical Analysis and Scientific Computing)

"Numerics-Informed Neural Networks for Parabolic Partial Differential Equations" by George Chumbipuma (15 - Numerical Analysis and Scientific Computing)

"Numerical Analysis of Transient Instability: A Pseudospectra Approach in Convection-Diffusion Matrices" by Adan Diaz (15 - Numerical Analysis and Scientific Computing)

"Numerical-Analytical Evidence for Convergence of the Semi-Discrete Lagrangian–Eulerian Method Applied to the Korteweg–de Vries Equation" by Erivaldo Diniz de Lima (15 - Numerical Analysis and Scientific Computing)

"Inverse Design of Magnetic Cloaks via Adjoint-Based PDE-Constrained Optimization" by Yusen Guo (15 - Numerical Analysis and Scientific Computing)

"Topological gradient-based methods for solving geometric inverse problems: theory and applications" by Maatoug Hassine (15 - Numerical Analysis and Scientific Computing)

"Multi-Resolution Wavelet-Augmented Physics-Informed Neural Networks for Efficient and Accurate Solutions of Complex Financial Differential Equations" by Kavita Kavita (15 - Numerical Analysis and Scientific Computing)

"Local Optimization of Weak Distance Between Compact Surfaces on Special Euclidean Group" by Kazuki Koga (15 - Numerical Analysis and Scientific Computing)

"Lyapunov Stability Analysis of a Uncertain Linear System" by Vanel Lazcano (15 - Numerical Analysis and Scientific Computing)

"Inverse Problem for a Parabolic Equation" by Fagueye Ndiaye (15 - Numerical Analysis and Scientific Computing)

"Bridging Scales in Choanoflagellate Hydrodynamics: Hybrid Model of Small-Colony Behavior" by Hoa Nguyen (15 - Numerical Analysis and Scientific Computing)

"Numerical Integrators for Disordered Multidimensional Hamiltonian Systems" by Bob Senyange (15 - Numerical Analysis and Scientific Computing)

"Numerical Investigation of Two-Dimensional Two-Phase Kelvin-Helmholtz Instability Problem" by Abdullah Shah (15 - Numerical Analysis and Scientific Computing)

"Numerical Study of Waves Generated by Landslides in U-Shaped Bays" by Rani Sulvianuri (15 - Numerical Analysis and Scientific Computing)

"Novel iterative Algorithm for Solving Equilibrium Problem with Applications to Optimal Control and 3D Image Processing" by Victor Uzor (15 - Numerical Analysis and Scientific Computing)

"A Semi-Discrete Lagrangian-Eulerian Scheme for Systems of 3D Hyperbolic Conservation Laws in Cubic Grids" by Pedro Henrique Valerio de Godoi (15 - Numerical Analysis and Scientific Computing)

"Total Controllability for Fractional Differential Systems with Impulsive Effects" by Rajesh Dhayal (16 - Control Theory and Optimization)

"Stabilization of Unstable Periodic Orbits via Delayed Feedback Controls" by Dohan Kim (16 - Control Theory and Optimization)

"FIRST-ORDER ALGORITHMS FOR STOCHASTIC MULTI-OBJECTIVE OPTIMIZATION PROBLEMS" by Yiyang Li (16 - Control Theory and Optimization)

"Modified Gradient Descent Methods for Coupled-Constrained Minimization and Quasi-Variational Inequalities" by Nevena Mijajlovic (16 - Control Theory and Optimization)

"Negative Stepsizes Make Gradient-Descent-Ascent Converge" by Henry Shugart (16 - Control Theory and Optimization)

"Solution Theory for Singular Linear Switched Systems in Discrete Time" by Sutrisno Sutrisno (16 - Control Theory and Optimization)

"Dimension, Dynamics, and Comparison in C*-Algebras" by M. Ali Asadi-Vasfi (9 - Dynamics)

12:10 PM – 12:30 PM 119-AB Short Communications

A Singular Perturbation Approach to Vector Fields on Manifolds with Boundary

In this talk, we propose a novel approach to studying vector fields defined on a manifold $\mathcal{M}$ with boundary by interpreting them as singularly perturbed vector fields whose phase space is forward invariant. In our framework, the boundary of $\mathcal{M}$ is approximated by compact subsets of a normally hyperbolic invariant manifold in the context of geometric singular perturbation theory. The key idea is to replace the lack of smoothness of the vector field on $\partial \mathcal{M}$ with a non-smooth system defined in the interior of $\mathcal{M}$. We then apply a regularization procedure to obtain a smooth singularly perturbed vector field that preserves the desired dynamical properties. The results establish an important connection among vector fields defined on manifolds with boundary, non-smooth vector fields, and singularly perturbed ones, and provide a way to treat the boundary of the phase space as a normally hyperbolic manifold, allowing the use of classical results such as those from Fenichel theory.
12:10 PM – 12:30 PM 118-C Short Communications

Generalized Sequence Spaces in the Bicomplex Framework

AbstractThis presentation focuses on generalizing classical sequence spaces to the bicomplex setting, where sequences consist of bicomplex numbers. We study their structural properties, including convergence and summability. We also explore how classical results extend or differ in this richer framework. Using the idempotent representation, we examine zero divisors and show how complex-valued results appear as special cases. This talk not only broadens the scope of existing sequence space theory but also suggests potential applications in bicomplex analysis and related mathematical areas.Keywords: Bicomplex numbers, Sequence spaces, Convergence and summability, Idempotent representation, Zero divisors.
12:10 PM – 12:30 PM 118-AB Short Communications

Hitting Primes by Dice Rolls

Let $S=(d_1,d_2,d_3, \ldots )$ be an infinite sequence of rolls ofindependent fair dice. For an integer $k \geq 1$, let $L_k=L_k(S)$be the smallest $i$ so that there are $k$ integers $j \leq i$ for which$\sum_{t=1}^j d_t$ is a prime. Therefore, $L_k$ is the random variable whose value is the number of dice rolls required until theaccumulated sum equals a prime $k$ times. We first compute the expectation and the variance of $L_1$ up to an additive error of less than $10^{-4}$ . The proof is simple, combining a basic dynamic programming algorithm with a quick Matlab computation and basic facts about the distribution of primes.Next, we show that for large $k$, the expected value of $L_k$ is $(1+o(1)) k\log_e k$, where the $o(1)$-term tends to zero as $k$ tends to infinity.Joint works with Noga Alon, Lucy Martinez, Doron Zeilberger
12:10 PM – 12:30 PM 120-AB Short Communications

Invariant States on Holonomy-Flux Algebras

Representations of canonical commutation relations are fundamental for quantum theory. In quantum mechanics, the celebrated Stone-von Neumann theorem shows that, given mild regularity conditions, there is only one representation (up to unitary equivalence). While this is, in general, no longer true in quantum field theory, uniqueness may still be given in the presence of symmetries. So, in loop quantum gravity, diffeomorphism invariance is well known to imply uniqueness of states on the so-called holonomy-flux algebra. The corresponding proof by Lewandowski et al., however, is very lengthy and technical. In our talk, we are going to present a drastically shorter proof of a more general uniqueness theorem we have obtained recently. This even applies to respective cosmological models.To be specific, consider some set $\mathfrak{F}$ of bounded functions on the configuration space and the unital $C^\ast$-algebra $\mathfrak{A}$ it generates. Moreover, let $\mathfrak{B} \supset \mathfrak{F}$ be a unital subalgebra of $\mathfrak{A}$, and let $\mathfrak{X}$ be a set of selfadjoint derivations (usually generated by Poisson brackets with certain momenta) on $\mathfrak{B}$. The holonomy-flux $\ast$-algebra $\mathfrak{H}$ is generated by $\mathfrak{B}$ and $\mathfrak{X}$, factorized by the commutation relations. Then, there is at most one state on $\mathfrak{H}$ that fulfills the following two conditions:a) The algebraic one requires that (i) $\mathfrak{X}(\mathfrak{F})$ and $1$ span a dense subset of $\mathfrak{B}$ and (ii) the elements of $\mathfrak{X}$ fulfill the chain rule if applied to $g \circ f$ for $f \in \mathfrak{B}$ and certain analytic $g$.b) The geometric one requires the state to vanish on each $X^2$ with $X \in \mathfrak{X}$. While the algebraic condition usually is a matter of collecting sufficiently "smooth" functions in $\mathfrak{B}$, the geometric condition is typically given for states that are invariant under symmetries. In particular, states that are invariant under semianalytic diffeomorphisms (for full loop quantum gravity) or under dilations (for homogeneous isotropic loop quantum cosmology) meet this requirement.
12:10 PM – 12:30 PM 116-A Short Communications

Neural Network Observers for a Forced Localization Task in Undersampled MRI

Modelling human performance in forced localization tasks is a challenge for anthropomorphic model observers because of the many possible locations along with capturing human perception and variability. This is particularly challenging in anatomical images where the modeling requires generalization to out-of-distribution images such as in varying undersampling in magnetic resonance imaging (MRI). In this study, we modeled human forced localization (FL) performance using images with varied percentage of low frequencies fully collected in 5X MRI undersampling, ranging from 0% (aliasing) to 20% (blurring). We used a modified EfficientNet-B1 architecture trained to directly predict coordinates (FLNet) as well as using a biologically inspired V1Block, which incorporates Gabor filters to mimic early stages of human visual processing as a preprocessing to FLNet (V1FLNet). We used additive noise in FLNet and Poisson noise in the channel outputs of V1FLNet to match human performance. When trained on images with a specific number of low frequencies collected, both neural networks surpassed average human accuracy but diverged from human-like performance on out-of-distribution data. Training on both 0% and 20% data, leading to interpolation in the generalization led to better results than training on one condition. An adaptive model which trained at all frequencies but was only matched at 20% for human data did the best in terms of modeling human performance. In this study, we were able to surpass and predict average human performance. Both models predicted the decrease in performance for the fully aliased image. V1FLNet in its current implementation had similar generalizability as FLNet.
12:10 PM – 12:30 PM 115-A Short Communications

Numerical Semigroups of Sally Type

A numerical semigroup S is called Sally type if its multiplicity is one more than its width. In this talk, we will analyze the properties of numerical semigroups of Sally type with embedding dimension $e-1$ and $e-2$ where $e$ denotes the multiplicity. We compute the minimal number of generators of the defining ideal together with the minimal generators and minimal graded free resolutions in some special cases.
12:10 PM – 12:30 PM 115-B Short Communications

Some Algorithmically Easy and Hard Problems in Knot Theory

Many classical knot theory problems can be formulated as decision problems. Quite a few of them are now known to lie in complexity classes NP or co-NP. At the same time, only several knot theory problems are known to be NP-hard, and even fewer non-trivial knot theory problems are known to have a polynomial algorithm. We will discuss two new such results: diagrammatic unknotting number being NP-hard (joint with Jaeyun Bae), and alternating link equivalence having polynomial complexity, when alternating diagrams are given (joint with Touseef Haider). Note that unknotting number (by crossing changes) has been particularly resistant to establishing any complexity bounds, with neither upper nor lower ones previously known. The proofs use tools from low-dimensional topology, at times mixing them with algorithmic complexity theory and topological graph theory.
12:10 PM – 12:30 PM 115-C Short Communications

The Grandeur and the Sorrow Behind the First Set-Theoretical Paper and the Emergence of the Dedekind Letters

This talk presents a detailed analysis of the circumstances that lead to Georg Cantor’s first paper on set theory in 1874. Particular attention is paid to Cantor’s correspondence with Richard Dedekind and the exchange of ideas between the two scholars. The undisclosed use of remarks of Dedekind’s in Cantor’s 1874 paper led to tensions and a tacit dispute over the authorship of the mathematical results contained therein. In this context, this talk announces the discovery of the Dedekind letters of Cantor’s Nachlass, which were believed to be lost. Two of those unedited letters from 1873 were used to confirm that some of the mathematical results in Cantor's 1874 paper were due to Dedekind. This matter, although very probable, had not yet been definitively confirmed and has led to greater tensions among historians who have dealt with Cantor and Dedekind.Further analyses of the relationship between the two mathematicians, the development of the mathematical ideas, and the authorship of the 1874 article are presented.
12:30 PM – 12:50 PM 115-B Short Communications

C-Chain Connectedness

Let $\mathcal{U}$ be an open covering of the topological space $X$ in $X$, $C\subseteq X$ and $x,y\in X$. A chain in $\mathcal{U}$ that connects $x$ and $y$ is a finite sequence of elements of $\mathcal{U}$ such that $x$ belongs to the first element of the sequence, $y$ to the last, and intersection of any two consecutive elements of the chain is nonempty. The set $C$ is totally weakly chain separated in $X$ if for every two distinct points $x,y\in C$ there exists an open covering $\mathcal{U}=\mathcal{U}_{xy}$ of $X$ such that there is no chain in $\mathcal{U}$ that connects $x$ and $y$. The set $C$ is totally chain separated in $X$ if there exists an open covering $\mathcal{U}$ of $X$ such that for every two distinct points $x,y\in C$ there is no chain in $\mathcal{U}$ that connects $x$ and $y$. The set $C$ is C-chain connected in $X$, if for every clopen (closed and open) covering $\mathcal{U}$ of $X$ and every $x,y\in C$, there exists a chain in $\mathcal{U}$ that connects $x$ and $y$. Let $A$ and $B$ be nonempty subsets of $X$. The sets $A$ and $B$ are C-weakly chain separated in $X$, if for every point $x\in A$ and every $y\in B$, there exists a clopen covering $\mathcal{U}=\mathcal{U}_{xy}$ of $X$ such that there is no chain in $\mathcal{U}$ that connects $x$ and $y$. The sets $A$ and $B$ are C-chain separated in $X$, if there exists a clopen covering $\mathcal{U}$ of $X$ such that for every point $x\in X$ and every $y\in Y$, there is no chain in $\mathcal{U}$ that connects $x$ and $y$. In this presentation we will study the properties of those sets. We will formulate statements in which the notions of C-chain connectedness, homotopy, and shape appear. Furthermore we will define analog notions for one previously given open or clopen covering. At the end we will define analog notions in a more general space then a topological.
12:30 PM – 12:50 PM 115-A Short Communications

Classification of 4-dimensional Hom-Lie Algebras

In this work we consider complex multiplicative Hom-Lie algebras of dimension 4 associated with non-nilpotent linear maps. We prove that for this class of algebras we can always obtain a 3-dimensional multiplicative Hom-Lie subalgebra. This allows us to obtain the full classification of these 4-dimensional Hom-Lie algebras.This is a joint work with Sonia Vera from Universidad Nacional de Córdoba.
12:30 PM – 12:50 PM 118-C Short Communications

Existence of Weak Solutions for Nonlinear Drift-Diffusion Equations with Measure Data

In this talk, we study nonlinear drift-diffusion equations of porous medium and fast diffusion types with a measure-valued external force. We first consider the case without drift to emphasize the influence of measure data and the nonlinear diffusion structure. Then, we establish the existence of nonnegative weak solutions that satisfy suitable gradient estimates when the drift term belongs to a sub-scaling class associated with the $L^1$ space. For divergence-free drifts, this requirement can be further relaxed to a scaling class, allowing a broader range of nonlinear diffusion behaviors.
12:30 PM – 12:50 PM 116-A Short Communications

Hyperfinite Neural Networks

We study neural networks with infinite width by modeling the width with a hyperfinite number from nonstandard analysis. Such hyperfinite neural networks, when trained for a hyperfinite amount of time via gradient descent (with respect to the square loss) with an infinitesimal step size, allow us to recover results about the neural tangent kernel (NTK), while providing new perspectives about them. In particular, our method allows us to transfer approximate versions of infinite-width NTK results to the situation of finite networks of large (finite) widths. These results offer a first basis of the use of nonstandard methods in machine learning, which we expect will be used to build further results in the NTK and deep learning literature.
12:30 PM – 1:30 PM Breaks

Lunch on Own

12:30 PM – 12:50 PM 120-AB Short Communications

On the Cohomology of Homogeneous Spaces of Lie Groups

The study of the de Rham cohomology of a homogeneous space G/H, where G is a connected Lie group and H is a closed subgroup, in relation to the algebraic invariants of G, H, and the inclusion of H into G, is a classical theme in differential geometry and topology.In this talk, I will present explicit descriptions of certain low-dimensional Betti numbers of homogeneous spaces of Lie groups. As an application, we obtain an interesting invariant of compact homogeneous spaces expressed in terms of the numbers of simple factors of the ambient group and of the associated closed subgroup. From a computational point of view, these descriptions are new and very useful, and they play an important role in determining the cohomology of nilpotent orbits; the talk is based on joint work with Indranil Biswas and Pralay Chatterjee.
12:30 PM – 12:50 PM 118-AB Short Communications

Propagation Phenomenon for Parabolic Equations with Memory and Its Application to Observability

In this talk, we present the propagation of singularities for parabolic equations with memory, which reveals how singularities of solutions propagate bidirectionally along the time direction. To analyze this property, we develop a parabolic-hyperbolic decomposition method. As a key application, we establish an exact two-sided observability inequality, which allows the stable reconstruction of initial data—in an optimal Sobolev space—from partial measurements. Moreover, we derive a a necessary and sufficient geometric condition on the observation domain for such observability inequality to hold. This talk is based on joint works with Gengsheng Wang and Enrique Zuazua.
12:30 PM – 1:30 PM Benjamin Franklin Stage Films @ ICM

Solving the Bonnet Problem

Film Directed by Ekaterina Eremenko 

For the first time, you can witness a complex mathematical problem being solved in front of your eye and understand some of the missteps, breakthroughs and successes.

The documentary "Solving the Bonnet Problem" follows the work of three mathematicians as they collaborate to solve a long-standing geometrical problem proposed by Pierre Ossian-Bonnet. Alongside their work, the film explores the lives and contributions of Bonnet and his contemporary Gaston Darboux, as well as the history of French mathematics in the 19th century. Captivating computer graphics help unravel intricate concepts and make them accessible to all.

Source: Discretization in Geometry and Dynamics

12:30 PM – 12:50 PM 115-C Short Communications

The Isoperimetric Problem for Hyperideal Polyhedra

In this talk, I will discuss the isoperimetric problem for hyperbolic hyperideal polyhedra. A convex hyperideal polyhedron, with all vertices beyond the sphere at infinity and equal edge lengths, uniquely maximizes volume among those with the same combinatorial type and surface area. Constructed examples include hyperideal counterparts of all convex uniform polyhedra, certain Johnson solids, and other hyperideal polyhedra with no analogues in Euclidean space.
12:30 PM – 12:50 PM 119-AB Short Communications

Vertex-Pancyclism in Edge-Colored Complete Graphs with Restrictions in Color Transitions

Let H be a graph possibly with loops and G a simple graph. We say that G is an H-colored graph whenever every edge of G has assigned a vertex of H as a color. A cycle C in an H-colored graph G is an H-cycle if and only if the colors of consecutive edges in C are adjacent vertices in H, including the last and first edges of C. An H-colored graph G is said to be vertex H-pancyclic if every vertex of G is contained in an H-cycle of length l for every l in {3,...,|V(G)|}.In this talk, we show sufficient conditions for an H-colored complete graph G to be vertex H-pancyclic.

12:50 PM – 1:10 PM 118-C Short Communications

A Nonlocal Problem for a Second-Order Hyperbolic Partial Integro-Differential Equation with Functional Terms

In this talk, I will discuss nonlocal problem for a second-order hyperbolic partial integro-differential equation with functional terms. Issues of existence, uniqueness, and construction of solutions to the nonlocal problem are investigated. By introducing new unknown functions, the original problem is reduced to a family of problems for first-order integro-differential equations with unknown parameters and integral constraints. An algorithm for constructing solutions to this family of problems is proposed, and its convergence is proved. Sufficient conditions for the existence and uniqueness of solutions to the family of first-order integro-differential problems with unknown parameters and integral constraints are established. Based on the relationship between the nonlocal problem and the corresponding family of problems, conditions for the unique solvability of the nonlocal problem for the second-order hyperbolic partial integro-differential equation with functional terms are obtained.{\it This research is funded by the Science Committee of the Ministry of Science and Higher Education of the Republic of Kazakhstan (Grant No. AP23485509).}
12:50 PM – 1:10 PM 118-AB Short Communications

An Integrated Approach on the Flow Increment Facility Location Problem Under Budget Constraint

The frequency of natural and human-induced disasters has been increasing and we are always under threat. This has led to a strong need for evacuation planning that is not only efficient but also able to guarantee the safety of the people, other living beings, property, and the ecosystem. The designing of evacuation strategies is the process of making decisions concerning to the objectives that are multiple and, in most cases, conflicting, for example, the minimizing of total evacuation time, the optimizing of the number of people that has to be shifted at safe places, and the providing of support facilities, which are essential, under limited resources within the heterogeneous type of integrated evacuation network. The research work here demonstrates a comprehensive framework of evacuation optimization that integrates multi-objective network flow concepts at its core. The model put forward is the one that determines in a joint manner the most advantageous locations of the facilities as well as the flow assignments to realize not only the evacuation that is efficient but also balanced. Moreover, to elevate network performance to even higher levels, a cost-aware contraflow strategy is presented which, by considering the switching and traffic management costs, along with the increasing capacity, reverses the arcs that are unused so as to facilitate the flow of traffic in an integrated approach. The inclusion of these genuine constraints in the model provides a means to evaluate the compromises that exist between efficiency, cost, and the feasibility of operations during disaster response.
12:50 PM – 1:10 PM 116-A Short Communications

Bolstering Stochastic Gradient Descent with Model Building

Stochastic gradient descent method and its variants constitute the core optimization algorithms that achieve good convergence rates for solving machine learning problems. These rates are obtained especially when these algorithms are fine-tuned for the application at hand. Although this tuning process can require large computational costs, recent work has shown that these costs can be reduced by line search methods that iteratively adjust the step length. We propose an alternative approach to stochastic line search by using a new algorithm based on forward step model building. This model building step incorporates second-order information that allows adjusting not only the step length but also the search direction. Noting that deep learning model parameters come in groups (layers of tensors), our method builds its model and calculates a new step for each parameter group. This novel diagonalization approach makes the selected step lengths adaptive.
12:50 PM – 1:10 PM 120-AB Short Communications

Characterization of Generalized Lie-Type Derivations on Algebras

Let $\mathcal{A}$ be an algebra over a commutative unital ring $\mathcal{R}.$For any $x_1,x_2,\ldots, x_n\in\mathcal{A},$ define $p_1(x_1)= x_1,$ $p_2(x_1,x_2)=[x_1,x_2]$ and$p_n(x_1, x_2,\ldots,x_n)= [p_{n-1}(x_1,x_2,\ldots,x_{n-1}),x_n]$ for all integers $n\geq{2},$ where $[x_1,x_2]=x_1x_2-x_2x_1$ denotes the Lieproduct of $x_1$ and $x_2$ in $\mathcal{A}$.An $\mathcal{R}$-linear mapping $\delta:\mathcal{A}\rightarrow\mathcal{A}$ is said to be a \textit{Lie $n$-derivation} ($n\geq{2}$) if$\delta(p_{n}(x_{1},x_{2},\ldots,x_{n})) = p_{n}(\delta(x_{1}),x_{2},\ldots,x_{n})+p_{n}(x_1, \delta(x_{2}),\ldots,x_{n}) +\cdots +p_{n}(x_1,x_{2},\ldots,\delta(x_{n}))$ holds for all $x_{1},x_{2},\ldots,x_{n}\in\mathcal{A}.$Lie $n$-derivations have been further generalized as follows:Let $\xi:\mathcal{A}\rightarrow\mathcal{A}$ be an $\mathcal{R}$-linear mapping and $\delta$ be a Lie $n$-derivation on $\mathcal{A}$.Then $\xi$ is called a generalized Lie $n$-derivation associated with the Lie $n$-derivation $\delta$ if$\xi(p_{n}(x_{1},x_{2},\ldots,x_{n})) = p_{n}(\xi(x_{1}),x_{2},\ldots,x_{n})+p_{n}(x_1, \delta(x_{2}),\ldots,x_{n}) +\cdots +p_{n}(x_1,x_{2},\ldots,\delta(x_{n}))$ holds for all $x_{1},x_{2},\ldots,x_{n}\in\mathcal{A}.$ For $n=2$, $\xi$ is said to be a generalized Lie derivation while for $n=3$, $\xi$ is called generalized Lie triple derivation. Generalized Lie derivation, generalized Lie triple derivation, generalized Lie $n$-derivation are collectively known as generalized Lie-type derivation.The study of the Lie structure of an associative algebra is one of the important topics in mathematics.In the present talk, we shall discuss characterization of generalized Lie-type derivations and related mappings on algebras and finally some potential future research problems in this direction will also be provided.
12:50 PM – 1:10 PM 115-C Short Communications

Einstein Metrics on Spheres

In this talk we give a brief introduction to the topic of Einstein metrics on spheres. In particular, we explain the existence of three non-round Einstein metrics with positive scalar curvature on the ten-dimensional sphere $S^{10}.$ Previously, the only even-dimensional spheres known to admit non-round Einstein metrics were $S^6$ and $S^8.$ This talk is based on joint work with Jan Nienhaus.
12:50 PM – 1:10 PM 115-B Short Communications

Fast Euclidean Embeddings for Projective Spaces and Lens Spaces

Whitney's embedding theorem guarantees any compact smooth manifold of dimension $n$ may be smoothly embedded into $\mathbb{R}^{2n}$. Hopf and James have provided embeddings for the real, complex, and quaternionic projective spaces which realize the dimension bound, but may require on the order of $n^2$ operations to compute a point. We show variants of these embeddings cost on the order of $n\log(n)$ operations per point, using the Fast Fourier transform. Using these embeddings, we can also construct embeddings for the lens spaces into dimension $Cn$ that cost on the order of $Cn\log(n)$ with $C$ a constant that depends on the action of $\mathbb{Z}/(m\mathbb{Z})$ used. When the lens space admits a large symmetry group, $C$ is close to 3, but when the symmetry group is small, $C$ may approach $n$. Giving each of the spaces a real-analytic semi-algebraic structure as abstract manifolds, our embeddings are real-analytic semi-algebraic, as they are induced by polynomial maps on the corresponding spheres.
12:50 PM – 1:10 PM 115-A Short Communications

On Compatible Leibniz Algebras

In this talk, we study the notion of compatible Leibniz algebras. We explore the classification of complex Leibniz algebras in dimensions two and three in order to obtain explicit examples of compatible pairs. We further characterize compatible Leibniz algebras in terms of Maurer-Cartan elements of a suitable differential graded Lie algebra. Moreover, we introduce a cohomology theory for compatible Leibniz algebras, which, in particular, governs one-parameter formal deformations of this algebraic structure. Motivated by classical applications of cohomology, we also investigate abelian extensions of compatible Leibniz algebras.
12:50 PM – 1:10 PM 119-AB Short Communications

The Strong 3-rainbow Index of Graphs

The concept of a strong 3-rainbow index, first introduced by Awanis and Salman (2022), is a refinement of the classical 3-rainbow index that imposes a stronger connectivity requirement. Specifically, it requires that every set of three vertices in a connected graph be connected by a rainbow Steiner tree of minimum size. This concept is motivated by applications in secure and efficient communication networks and leads to computationally challenging problems, as determining the strong 3-rainbow index is NP-hard in general.In this work, we establish the exact values of the strong 3-rainbow index for several classes of graphs, as well as for graphs obtained through certain graph operations. Moreover, we characterize graphs for which this parameter attains certain values. These results contribute to a deeper understanding of strong 3-rainbow coloring and its relationship with graph structure and complexity. Furthermore, they provide a solid foundation for future investigations into generalized strong k-rainbow indices and their potential applications in the design of secure and efficient communication networks.
1:10 PM – 1:30 PM 119-AB Short Communications

Edge Compound Constructions and Ramsey Minimality for Disjoint Stars

A graph $F$ is {\em Ramsey $(G,H)$-minimal} if every red-blue edge coloring of $F$ contains a red copy of $G$ or a blue copy of $H$, yet this property is lost upon deleting any single edge. Such graphs represent extremal witnesses of unavoidable structure in Ramsey theory.We develop a unified construction of Ramsey $(nK_{1,2},H)$-minimal graphs for arbitrary $n\ge 1$ and any 2-connected graph $H$. The approach is based on an edge–compound method, where edges of a backbone graph are replaced by suitable Ramsey blocks. An orientation-based admissibility condition on the backbone provides a transparent criterion for both the Ramsey property and minimality.This framework yields infinite families of Ramsey minimal graphs, encompassing cycles and generalized theta graphs, and subsumes several earlier constructions within a single structural perspective. The results illuminate how local coloring constraints and global graph structure interact to force disjoint stars, offering new insight into the fine structure underlying Ramsey minimality.
1:10 PM – 1:30 PM 115-B Short Communications

Knotted Handlebodies and Dehn Surgery on Knots

Many years ago the author decribed a family of hyperbolic knots having a half-integral toroidal surgery, that is, a surgery producing a manifod that contains an incompressible torus, hence a non-hyperbolic manifold. The important point in this construction is that the surgery coefficient is non-integral. Later, Gordon and Luecke proved that such a family consists of all hyperbolic knots that admit a non-integral toroidal surgery.However, this constuction was made by means of tangles and double branched covers, and then no explicit figure of the knots was given.Recently, the author has given an explicit constuction of some of the knots, and now will present an explicit construction of some infinite families of such knots.The construction is more or less as follows. Let H be a genus 2-handlebody embedded in the 3-sphere, which is knotted, that is, the bounday of its exterior is incompressible. Suppose that M is a Möbius band properly embedded in the exterior of H, such that the boundary of M intersects any meridian disk of H. Then it can be shown that the core of the Möbius band M is a knot K with a half-integral toroidal surgey. The surgery coefficient is determined by the intersection of M with a regular neighborhood of K.The difficult point is to find explicit figures of the handlebody H and the Möbius band M. We will show a procedure to find such explicit embeddings of handlebodies and Möbius bands.
1:10 PM – 1:30 PM 116-A Short Communications

Mathematics with Observers

Mathematics with Observers Nikolai Khots, Dmitriy Khots, Boris Khots ABSTRACT We give here short overview of the main parts of Mathematics with Observers, introduced on base of infinity idea denial. We introduce Observers into arithmetic, and arithmetic becomes dependent on Observers. And after that the basic mathematical parts also become dependent on Observers. We call Mathematics with Observers both Observers in arithmetic and the other parts of mathematics based on this arithmetic. We show that almost all classic geometry theorems are satisfied in Mathematics with Observers geometry with probabilities less than 1. We proved that same plane has couples (point and straight line not containing this point) where Euclidean geometry works, other couples where GaussBolyai-Lobachevsky geometry works, and other couples where Riemann geometry works Based on Physics data we developed Mathematics with Observers interpretation of the main laws of Fluid Mechanics, Yang-Mills theory. In particular, we make analysis of Navier-Stokes equations and solution existence of these equations. Mathematics with Observers allows us to treat the classic Maxwell and Yang-Mills equations as the stochastic equations. We proved solution existence of Yang-Mills equations. The currently open problem of the "mass gap existence" is solved in the frame of the new theory. ICM 2026 Short Communications Speaker - Nikolai Khots
1:10 PM – 1:30 PM 118-AB Short Communications

Pointwise Hölder Continuity of the Joint Spectral Radius and the Geometry of Extremal Norms

The joint spectral radius of a compact set of square matrices measures the exponential growth rate of the norm of long products from this set. Since its introduction by Rota and Strang in 1960, it found applications for example in the study of switched linear systems or the regularity of wavelets. It is also an interesting quantity from a purely theoretical point of view due to its connections with ergodic optimization and symbolic dynamics.A central dichotomy in its study is between reducible and irreducible matrix sets, which require fundamentally different techniques. A set is irreducible, if it admits no non-trivial jointly invariant subspace. In this case a key tool is provided by so-called extremal norms, i.e. the norms whose unit ball is jointly invariant under all matrices in the set, multiplied by the inverse of the joint spectral radius.Understanding the sensitivity of the joint spectral radius under perturbations is crucial in applications. In joint work with Fabian Wirth we proved that the joint spectral radius depends pointwise Hölder continuously on the matrix set. This generalizes both the single-matrix case, as well as Wirth's earlier results for the irreducible case, where local Lipschitz continuity holds. In dimension two we can even show local, instead of pointwise, Hölder continuity away from zero. The obstruction to extending our argument to higher dimensions is tied to the geometry of extremal norms and in particular to certain extremal projection constants from finite-dimensional Banach space theory. We will discuss both the methods behind the regularity results and the obstructions related to the projection constants.
1:10 PM – 1:30 PM 115-C Short Communications

Ricci Flow on ALF Manifolds

Following the seminal work of Hamilton and Perelman, Ricci flow has proved to be a powerful tool for understanding the topology and geometry of three-dimensional manifolds. A natural and fundamental question is whether Ricci flow can play a similar role in dimension four. In this work, we investigate the long-time behavior of Ricci flow on four-dimensional manifolds, with particular emphasis on Ricci-flat asymptotically locally flat (ALF) spaces. Ricci-flat ALF manifolds constitute the simplest class of collapsing Ricci-flat 4-manifolds and are widely expected, according to a folklore conjecture, to arise as singularity models in the long-time behavior of Ricci flow on 4-manifolds.We develop a framework for studying Ricci flow on ALF manifolds. First, we show that the ALF structure is preserved along the Ricci flow. We then introduce a renormalized version of Perelman's $\lambda$-functional adapted to the ALF setting, defined using a notion of relative mass with respect to a fixed Ricci-flat reference metric at infinity. Within this framework, we prove that the Ricci flow can be interpreted as the gradient flow of this adapted $\lambda$-functional in a weighted $L^2$ sense. This variational structure allows us to define and analyze notions of linear and dynamical stability for Ricci-flat ALF metrics.As an application, we show that conformally Kähler but non-hyperkähler Ricci-flat ALF metrics are dynamically unstable under the Ricci flow. This instability is significant from the perspective of long-time analysis, as it suggests that such metrics may be dynamically disfavored as singularity models. A key analytic ingredient is a Fredholm theory for the Laplacian operator on weighted Hölder spaces over ALF manifolds.Finally, our results point toward several open questions. In particular, it remains an open problem whether the relative mass introduced here satisfies positivity properties analogous to classical positive mass theorems. Moreover, recent constructions of new Ricci-flat ALF metrics raise the question of whether these examples are dynamically stable or unstable under Ricci flow.This is a joint work with Tristan Ozuch.
1:10 PM – 1:30 PM 120-AB Short Communications

The Projective Functors on the Category O

Bernstein and Gelfand classified the projective functors (i.e. direct summands of the tensor by a finite dimensional representation) on the category of Z-finite modules on 1980. We will discuss the restriction of the projective functors on the category O, and the connection to Soergel bimodules.
1:10 PM – 1:30 PM 118-C Short Communications

Very Weak Solutions of Dirac Operators with Distributional Coefficients

We discuss the possibility of studying very weak solutions for Dirac operators with distributional coefficients.The approach adapts classical tools from hypercomplex analysis, in particular the CK extension,to this low-regularity setting. These methods are combined with techniques developed by M. Ruzhansky and hiscollaborators for the analysis of partial differential equations with non-smooth coefficients.
1:10 PM – 1:30 PM 115-A Short Communications

Weyl Modules for Twisted Toroidal Lie Algebras

In this talk, we extend the notion of Weyl modules for twisted toroidal Lie algebra $\mathcal{T}(\mu)$. We prove that the level one global Weyl modules of $\mathcal{T}(\mu)$ are isomorphic to the tensor product of the level one representation of twisted affine Lie algebras and certain lattice vertex algebras. As a byproduct, we calculate the graded character of the level one local Weyl modules of $\mathcal{T}(\mu)$.
1:30 PM – 1:50 PM 118-AB Short Communications

D&A: Resource Optimisation in Personalised PageRank Computations Using Multi-Core Machines

Resource optimisation is commonly used in workload management, ensuring efficient and timely task completion utilising available resources. It serves to minimise costs, prompting the development of numerous algorithms tailored to this end. The majority of these techniques focus on scheduling and executing workloads effectively within the provided resource constraints. In this talk, we tackle this problem using another approach. We propose a novel framework D\&A to determine the number of cores required in completing a workload under time constraint. We first preprocess a small portion of queries to derive the number of required slots, allowing for the allocation of the remaining workloads into each slot. We introduce a scaling factor in handling the time fluctuation issue caused by random functions. We further establish a lower bound of the number of cores required under this scenario, serving as a baseline for comparison purposes. We examine the framework by computing personalised PageRank values involving intensive computations. Our experimental results show that D&A surpasses the baseline, achieving reductions in the required number of cores ranging from $ 38.89\% $ to $ 73.68\% $ across benchmark datasets comprising millions of vertices and edges.
1:30 PM – 1:50 PM 115-C Short Communications

Geometric Potential of Surfaces in Euclidean Spaces

In the present study, we considered skew curvatures of the surfaces to generate their geometric potentials. The method depends essentially on the mean and Gaussian curvatures and their principal curvatures. In quantum mechanics in the study of the dynamics of massive particle with mass $m$ constrained to move on a surface. In such a case, the difference function of the squared mean curvature with the Gaussian curvature induces a geometric (scalar) potential. This potential appears in the Shröndiger type equations. Considering the skew curvatures of the rotational surfaces, some results on the meridian curves are obtained. The term "geometric potential" in the context of rotational surfaces often relates to the functional or energy that describes certain properties of these surfaces. The geometric potential of rotational surfaces encompasses various functionals and energies related to their geometry. Furthermore, the geometric potentials of level surfaces and generalized helicoidal surfaces are calculated. Finally we discuss the some applications of these types of surfaces in quantum mechanics.
1:30 PM – 1:50 PM 120-AB Short Communications

Linkage Principle for Small Quantum Groups

We consider small quantum groups with root systems of Cartan, super and modular type, among others. These are constructed as Drinfeld doubles of finite-dimensional Nichols algebras of diagonal type. We discuss their connections with other algebras in the literature and highlight distinctive features of their representation theory. Based on the homonymous work by the author [Adv. Math. 475 (2025) 110347], we prove a linkage principle for them by adapting techniques from the work of Andersen, Jantzen and Soergel in the context of Lusztig’s small quantum groups. As a consequence, we characterize the blocks of the category of modules. We also introduce a notion of (a)typicality analogous to that appearing in the representation theory of Lie superalgebras. The typical simple modules turn out to be the simple and projective Verma modules. Moreover, we deduce a character formula for 1-atypical simple modules.
1:30 PM – 1:50 PM 115-A Short Communications

Permutation Orbifolds of Vertex Operator Algebras

A central problem in the theory of vertex operator algebras (VOAs) is the orbifold problem, which concerns the relationship between a VOA $V$ and its fixed-point subalgebra $V^G$ under the action of a finite automorphism group $G$. Understanding how the representation theory of $V$ relates to that of $V^G$ is fundamental to both the structure theory of VOAs and their connections with conformal field theory.In this talk, we focus on permutation orbifolds, arising from the natural action of the symmetric group $S_n$ on the tensor product $V^{\otimes n}$. Such orbifolds play an important role in the construction and classification of vertex operator algebras and conformal field theories. We discuss recent progress on the structure and representation theory of permutation orbifolds.
1:30 PM – 1:50 PM 118-C Short Communications

Strong Convergence of the Jacobian Determinant of a Regularised Flow Defined by a One-Sided Lipschitz Operator

In the context of the Cauchy problem for a multidimensional linear transport equation with smooth coefficient, solutions are known to depend on the characteristics curves, as well as for the associated conservation equation. More precisely, solutions of the conservation equation depend on the Jacobian determinant of the characteristic curves. However, the theory of characteristics is not working when the coefficient is not smooth. The notion of solution has to be reinvestigated. In the case where the coefficient satisfies the one-sided Lipschtiz condition, existence, uniqueness and weak stability of solutions has been established using the duality between the backward conservation problem and the advective forward problem. An open problem is the strong convergence of the Jacobian determinant of the regularised flow associated with the characteristics curves. This talk provides an answer to this question, which was posed 20 years ago.
1:30 PM – 1:50 PM 115-B Short Communications

Symplectic Rational Homology Ball Fillings of Seifert Fibered Spaces

We characterize when some small Seifert fibered spaces can be the convex boundaries of symplectic rational homology balls and give strong restrictions for others to bound such manifolds. (This is a joint work with J. B. Etnyre and B. Tosun.)
1:30 PM – 1:50 PM 116-A Short Communications

The History and Present of Infinitesimals

We discuss the history of infinitesimals in five periods. Then we find that a key problem is to establish a system dealing with infinitesimals. We further show that there may be a new approach to fundamentally solve this problem.(i) The rudiment of the idea of infinitesimals was born before calculus was established.(ii) Thanks to the use of infinitesimals, calculus methods had made great progress in the period of establishing and developing calculus.(iii) In the rigorization of analysis period, the mainstream modern calculus system was formed, in which differential (or infinitesimals) becomes unnecessary.(iv) Refactoring with a rigorous logical foundation, non-standard analysis showed that Leibniz’ use of infinitesimals was maintained.(v) Infinitesimal analysis is currently an active field featuring both mathematical innovations and historical re-appraisal.
1:30 PM – 1:50 PM 119-AB Short Communications

Vertex Energy for Extended Adjacency Matrix of a Graph and Some Newer Bounds

The extended adjacency matrix of a graph $G$ with $n$ vertices is defined as a real symmetric $n \times n$ matrix $\cal{A}$, where the $(i,j)$-th entry of ${\cal A}$ is given by the arithmetic mean of the ratio of the degrees of vertices $v_i$ and $v_j$ and its reciprocal if $v_i$ and $v_j$ are adjacent, and zero otherwise. Specifically, for adjacent vertices $v_i$ and $v_j$ with degrees $d_i$ and $d_j$, the entry is $\frac{1}{2} (\frac{d_i}{d_j} + \frac{d_j}{d_i})$. The extended energy of the graph is subsequently defined as the sum of the absolute values of the eigenvalues of this matrix. In the present work, we introduce the concept of extended vertex energy as the diagonal elements of the matrix $|{\cal A}|=\left({\cal A}^2\right)^{1/2}=Q|\Lambda|Q^T$, where $Q\Lambda Q^T$ is the spectral decomposition of $\cal{A}$. From there, we establish some new upper bounds of the extended energy of a graph involving order, size, largest, and smallest degree. We show that those are improvements of some existing bounds. Through direct manipulation, we obtain some more upper and lower bounds of the extended energy, which are either better or incomparable with the existing bounds. Finally, some improved bounds of the Nordhaus-Gaddum type are also presented.
2:00 PM – 3:45 PM Benjamin Franklin Stage Films @ ICM

Journeys of Black Mathematicians: Forging Resilience

Film Directed by George Csicsery

Journeys of Black Mathematicians: Forging Resilience is the first of a two-part documentary series produced by George Csicsery and Zala Films and developed in collaboration with Tatitana Toro.

Simons Laufer Mathematical Sciences Institute and Johnny Houston, NAM that traces the evolution of a culture of Black scholars, scientists and educators. The film follows the stories of prominent pioneers, the challenges they faced and their triumphs as they are reflected in the success and contributions of today's productive Black mathematicians who followed them.

Panelists

  • Dennis Davenport, Howard University
  • William Massey, Princeton University
  • Talithia Williams, Harvey Mudd College
  • Moderators: Johnny Houston and Aris Winger
2:00 PM – 6:00 PM Hall E - Expo Math Festival

Math Festival Day 1

Join us in Hall E for a family-friendly Math Festival open to the public. This interactive celebration of mathematics will feature hands-on activities, engaging talks, games and art designed to inspire curiosity and showcase the beauty and creativity of math for all ages. Discover how mathematics connects to everyday life, science, and culture while experiencing the excitement of one of the world’s largest gatherings of mathematicians.

MathHappens Activity Area

  • Multi-station interactive math playground featuring puzzles, tiles, and tactile models that encourage exploration, pattern recognition, and informal learning through hands-on discovery.

Maze Mat / Twist-n-Roll / Ring of Fire

  • Dynamic large-scale interactive math installations including floor-based mazes, tactile exhibits, and collaborative builds designed for full-body engagement and high visitor throughput.

Probability Power / Clothesline of Chance

  • Interactive game-show style probability experience where participants engage in live challenges (coin flipping + probability ranking) to build intuition around chance and real-world likelihood (close line).

Interactive Math Festival

  • Large-scale hands-on math festival environment featuring multiple table-based activities designed to spark curiosity, collaboration, and joyful problem-solving for K–8 audiences.

Are We There Yet? An Exploration of Distance

  • Immersive multi-model math exploration combining physical builds, interactive puzzles, and VR to demonstrate different concepts of distance and geometry across mathematical systems.

Math Card Game Exhibit

  • Interactive math card game experience connecting middle school math concepts to real-world scenarios through collaborative, play-based problem solving.

Sierpinski Simplices

  • Collaborative fractal-building activity where participants construct a large Sierpinski tetrahedron through hands-on assembly, illustrating patterns, scaling, and mathematical structure.
3:00 PM – 3:45 PM 119-AB Joint Section Lecture

Algebraic Correspondences and Schwarz Reflections: Where Rational Dynamics Meets Kleinian Groups

In this talk, we will give an overview of the fertile and rapidly developing field of algebraic correspondences in dynamics, with a particular focus on matings between rational maps and Kleinian groups. These appear in both the holomorphic and antiholomorphic worlds, arising from Schwarz reflection maps in the latter. We will explore how their parameter spaces unify moduli spaces of rational maps and Kleinian groups in a natural way. We will also highlight several applications of the techniques developed in this framework and share some open problems and promising directions for future research.
3:00 PM – 3:45 PM 115-A Joint Section Lecture

Conjugacy Width in Higher-Rank Arithmetic Groups

The width of a subset X in a group G is the diameter of the connected components of the Cayley graph Cay(G,X). In this talk, we will present a conjecture about widths of conjugacy classes in higher-rank arithmetic groups, provide evidence for its validity, and relate width of conjugacy classes to the Congruence Subgroup Property, Bounded Generation, Norm Rigidity, and Strong First-Order Rigidity.
3:00 PM – 3:45 PM 115-B Joint Section Lecture

Forcing Axioms and The Continuum Problem: Hilbert's First Problem Revisited

Georg Cantor famously proved in the 1870’s that there are more real numbers than natural numbers. A question is then “Exactly how many real numbers are there? \(\aleph_1\)? \(\aleph_2\)? Maybe more?” This is known as the Continuum Problem. It has been one of the most important guiding problems throughout the history of set theory. By work of Kurt Godel in the 1930’s and of Paul Cohen in the 1960’s we know that the standard axiomatic system for set theory, namely ZFC, does not solve this problem. On the other hand, and notwithstanding the independence results of Godel and Cohen, there are good reasons not to take the Continuum Problem as a pseudo-problem. In our talk we will start by hinting at some of the reasons not to take the independence results as the last word in this story. We will then introduce and motivate forcing axioms and will present some older and also some quite recent results using these axioms in order to argue that the Continuum Problem may have a solution after all. We will also mention some competing views and open questions in the area.
3:00 PM – 3:45 PM 121-AB Joint Section Lecture

Harmonic Maps in Singular Geometry and Rigidity

We will discuss results on harmonic maps into spaces of non-positive curvature, with a focus on targets that lack smooth structure. More precisely, we consider targets that are complete metric spaces with non-positive curvature in the sense of Alexandrov, commonly referred to as NPC (non-positively curved) or CAT(0) spaces. We discuss applications of harmonic maps to rigidity phenomena, including generalizations of Margulis superrigidity and the holomorphic rigidity of Teichmueller space. Our approach relies heavily on the regularity theory of harmonic maps to non-smooth targets, enabling differential-geometric techniques to be employed in the absence of any smooth structure on the target.
3:00 PM – 3:45 PM 122-AB Joint Section Lecture

Holonomy Bounds and Diophantine Approximation

The authors have proven a number of theorems concerning power series that simultaneously have nice arithmetic properties (the coefficients are integers or rational numbers with controlled denominators) and nice analytic properties (they have analytic continuations to large domains). These methods were originally devised to prove new irrationality results based on a method first used by Apéry to prove the irrationality of ζ(3). In this talk, we explore several threads arising from this work, including a number of new applications to effective Diophantine approximation and beyond.
3:00 PM – 4:30 PM 117-A IMU Panel

IMU Panel: Committee for Women in Mathematics

Finding and Defining Success in Mathematics:  Pathways and Measures

Mathematics has often emphasized a narrow vision of what a successful career can look like. This panel expands that horizon by celebrating the many dynamic ways success can emerge across research, leadership, industry, and public engagement. Bringing together diverse experiences, perspectives, and insights, the discussion will explore how mathematicians navigate, shape, and define success along different professional pathways.

We warmly invite the entire mathematical community to join this conversation, reflect together, and imagine even more paths forward. Our hope is to inspire broad and inclusive understandings of achievement and impact across our field.

This panel is jointly organized by the Association for Women in Mathematics (AWM) and the IMU Committee for Women in Mathematics (CWM). Co-organizers include Carolina Araujo, Hélène Barcelo, Raegan Higgins, Lakeshia Legette Jones, Darla Kremer and Elaine Pimentel.

Panelists:

  • Annalisa Crannell, Franklin & Marshall College
  • Fern Hunt, National Institute of Standards and Technology
  • Emily Riehl, Johns Hopkins University
  • Shelby Wilson, Johns Hopkins University

Moderators:

Carolina Araujo, Instituto Nacional de Matemática Pura e Aplicada

  • Darla Kremer, Association for Women in Mathematics

 

 

3:00 PM – 3:45 PM 115-C Section Lecture

Is Mathematics Education Responsive to Ecological Justice: with Embodied, Entangled, ‘Popular’ Knowledges?

A quarter of this century has passed by, through a devastating pandemic, and unprecedented ecological disasters, while education grapples with discourses of ‘21st century skills’. Do we better understand mathematics that can critically engage our children who live diverse lives - now and in the decades to follow? We interrogate the import of 21st century discourses for mathematics education, that reinforce hierarchies of ‘skills’ vs ‘knowledge’, to sort and segregate, and maintain a global division of work between the ‘ethereal’ and the material worlds. We bear witness to regimes of standardization and homogenization of mathematics curricula ascribing large populations of young people as “low performers”. Interdisciplinary studies of connected relationalities of knowledge and material production, inspire a recrafting of paradigms of mathematics education that invisibilize artisanal and ‘popular’ vernacular knowledges, and the livelihoods of those who have lived by the earth. Towards this end, we explore intercultural imaginaries and co-constructions of mathematics for school and work-based (not vocational) education, that are responsive to livelihoods, places and the planet, with a commitment to ecological justice.
3:00 PM – 5:00 PM Terrace Ballroom Roundtable / Panel

Panel: Mathematics for AI

This panel explores the relationship between mathematics and artificial intelligence, highlighting how mathematical ideas continue to shape the development and understanding of AI. Panelists will share perspectives on current trends, challenges, and opportunities at the intersection of these fields, offering insights for both technical and general audiences.

Moderator: Gigliola Staffilani, Massachusetts Institute of Technology 

Panelists:

  • Randall Balestriero, Brown University
  • Peter Barlett, University of California, Berkeley and Google DeepMind
  • Joan Bruna, New York University
  • Bin Yu, University of California, Berkeley

 

3:00 PM – 3:45 PM 118-C Section Lecture

Problems on Spherical Maximal Functions

We survey old and new results and conjectures on spherical maximal functions, emphasizing problems with a fractal dilation set.
3:00 PM – 3:45 PM 118-AB Section Lecture

Quantitative Hypocoercive Convergence Estimates for Underdamped Langevin Equations

The underdamped Langevin dynamics is perhaps one of the most familiar model used in sampling and non-equilibrium relaxation. Compared with its overdamped limit, the underdamped dynamics exhibits diffusive-to-ballistic acceleration of convergence. Nevertheless, quantifying such acceleration is challenging due to the degeneracy of diffusion. A large literature of hypocoercive estimates has been developed over the years to establish such quantitative rates. 

In this talk, we will discuss some recent progress in sharp convergence rate estimates for underdamped Langevin dynamics, in relative entropy and Renyi divergence, based on a modified entropy method and space-time log-Sobolev inequality respectively. 

3:00 PM – 3:45 PM 116-A Joint Section Lecture

Sampling Algorithms and High-Dimensional Expansion

I will present progress in designing fast algorithms for sampling combinatorial objects, based on the theory of high-dimensional expansion. This framework was first used on matroids, where, besides fast sampling, it also resolved a long-standing conjecture of Mihail and Vazirani on the expansion of matroid polytopes and another of Mason on ultra-log-concavity of independent set counts. Since then, this framework has been extended to many other combinatorial objects and distributions by developing new notions of high-dimensional expansion called spectral and entropic independence. I will survey the key tools developed in this area by showcasing applications to the sampling of several combinatorial objects: matroids, matchings, and Eulerian tours.

3:00 PM – 3:45 PM 120-AB Joint Section Lecture

Two Decades of Probabilistic Approach to Liouville Conformal Field Theory

Over the past twenty years, the probabilistic approach to Liouville Conformal Field Theory (LCFT) has undergone remarkable developments, transforming a collection of ideas at the interface of probability, geometry, complex analysis and physics into a coherent mathematical theory. Building on Gaussian Free Fields and Gaussian Multiplicative Chaos, rigorous definitions of correlation functions and partition functions have been established, culminating in the probabilistic derivation of the DOZZ formula and a mathematically complete formulation of the conformal bootstrap for LCFT on Riemann surfaces. This talk aims to provide a synthetic account of these advances, emphasizing both the main achievements and the open problems that continue to drive the field.
4:00 PM – 4:45 PM 115-B Joint Section Lecture

Anti-Classification Results in Ergodic Theory

We give a brief history of classification and anti-classification results in measure-theoretic and smooth ergodic theory. Then we describe our main result, which is an anti-classification theorem for isomorphism of ergodic measure-preserving flows up to a continuous time change, and we give a brief indication of the ideas in the argument. The general framework of the proof is the same as for the anti-classification result for ergodic automorphisms and flows (with no time change allowed) obtained by M. Foreman, D. Rudolph, and B. Weiss in 2011. The main difference between their work and ours is that we use methods from Kakutani equivalence theory to make our construction and to prove that certain pairs of transformations are not Kakutani equivalent. In addition, we describe anti-classification results for isomorphism that we obtain from these methods. This includes anti-classification for isomorphism in three settings: (1) sigma-finite measure-preserving ergodic automorphisms; (2) zero-entropy mixing automorphisms; (3) Kolmogorov-automorphisms. All of these results except (1) also hold for smooth diffeomorphisms preserving a smooth measure. The transfer to the smooth setting utilizes machinery developed by Foreman and Weiss. This talk is joint with Philipp Kunde.
4:00 PM – 4:45 PM 118-AB Section Lecture

Applied Random Matrix Theory

Random matrices now play a role in many parts of computational mathematics. To advance these applications, it is desirable to have tools that are flexible, easy to use, and powerful. Over the last 25 years, researchers have developed a remarkable family of results, called matrix concentration inequalities, that meet the criteria. This lecture offers an invitation to the field of matrix concentration and its multifarious applications.
4:00 PM – 4:45 PM 115-C Section Lecture

Calculation That Involves Neither Numbers Nor Formulas

These days news after news tout how machines imitate humans, but much of the history of calculation consists in humans pretending to be like machines. This is a magic show which discovers that, even outside any formalism, we can't help calculating. We'll discuss its importance when engaging in mathematical popularization and education for actual humans. (And you'll be able to perform the same magic later for friends and family.)
4:00 PM – 4:45 PM 115-A Section Lecture

Character Correspondents in Finite Groups

Two of the most important conjectures in the representation theory of finite groups have been recently proven: Richard Brauer’s Height Zero Conjecture (1955) and John McKay’s Degree Conjecture (1971). The proofs of both rely on the Classification of Finite Simple Groups. A key idea in their resolution has been to associate, to each irreducible character of a simple group, another character of a local subgroup that, remarkably, behaves in a corresponding way. This was proposed by M. Isaacs, G. Malle and this author in 2007.In the case of the McKay Conjecture, it took nearly 20 years to fully verify this correspondence, a milestone finally achieved by M. Cabanes and B. Späth. A similar strategy was applied to Brauer’s Height Zero Conjecture for the prime 2 by L. Ruhstorfer, after the so called Gluck--Wolf--Navarro--Tiep theorem was proved, and a reduction of B. Späth and this author. For odd primes, however, G. Malle, A. Schaeffer-Fry, P. H. Tiep, and the present author had to develop an entirely different approach to finally establish the result.This idea of character correspondents is now being extended to tackle other global/local conjectures, including Alperin’s Weight Conjecture, several refinements of the McKay Conjecture, and even Feit’s Conjecture on fields of values. The purpose of this talk is to explain these developments in greater detail.
4:00 PM – 4:45 PM 119-AB Joint Section Lecture

Integrable Billiards and Related Topics

In this talk we will survey our results on integrable billiards. We consider various models of billiards, including Birkhoff, outer, magnetic, and Minkowski billiards. Also, we discuss wire billiards and billiards in cones. For four models of convex plane billiards, we also discuss an isoperimetric-type inequality for the Mather \(\beta\)-function. We conclude with natural open questions on this subject. Joint talk with Misha Bialy.
4:00 PM – 4:45 PM 118-C Section Lecture

Multi-Bubble Isoperimetric Problems

The classical isoperimetric inequality in Euclidean space Rn states that among all sets of prescribed volume, the Euclidean ball (uniquely) minimizes surface area, explaining why a single soap bubble is always a round sphere. One may similarly consider isoperimetric problems on more general metric-measure spaces, such as on the n-sphere Sn and on n-dimensional Gaussian space Gn (i.e. Rn endowed with the standard Gaussian measure). More generally, we consider the multi-bubble isoperimetric problem, in which one prescribes the volumes of k >= 2 bubbles and minimizes their total surface area -– as any mutual interface will only be counted once, the bubbles are thus incentivized to clump together. The double-bubble problem (case k=2) on R3 was resolved by Hutchings, Morgan, Ritoré  and Ros in 2000. We survey recent advancements in the characterization of multi-bubble isoperimetric minimizers on Gn, Rn and Sn, as well as the stability of soap bubble partitions. Based on joint works with Joe Neeman and Botong Xu. There will be many pictures!
4:00 PM – 5:00 PM Hall E - Expo Poster Presentations

Poster Presentation by Author

"Heat Regulation Model in the Human Body During Cycling due to the Met-Abolic Effect" by Saraswati Acharya (15 - Numerical Analysis and Scientific Computing)

"Preconditioned Iterative Methods and Sensitivity Analysis for a Class of Saddle Point Problems" by Sk Safique Ahmad (15 - Numerical Analysis and Scientific Computing)

"Lambda admissible subspaces of self adjoint matrices" by Francisco Arrieta Zuccalli (15 - Numerical Analysis and Scientific Computing)

"Efficient Numerical Implementation of a Stochastic Time-Fractional Coupled Flow Model" by Abdumauvlen Berdyshev (15 - Numerical Analysis and Scientific Computing)

"A Poisson-Nernst-Planck Single Ion Channel Model and its Effective Finite Element Solver" by Zhen Chao (15 - Numerical Analysis and Scientific Computing)

"Numerics-Informed Neural Networks for Parabolic Partial Differential Equations" by George Chumbipuma (15 - Numerical Analysis and Scientific Computing)

"Numerical Analysis of Transient Instability: A Pseudospectra Approach in Convection-Diffusion Matrices" by Adan Diaz (15 - Numerical Analysis and Scientific Computing)

"Numerical-Analytical Evidence for Convergence of the Semi-Discrete Lagrangian–Eulerian Method Applied to the Korteweg–de Vries Equation" by Erivaldo Diniz de Lima (15 - Numerical Analysis and Scientific Computing)

"Inverse Design of Magnetic Cloaks via Adjoint-Based PDE-Constrained Optimization" by Yusen Guo (15 - Numerical Analysis and Scientific Computing)

"Topological gradient-based methods for solving geometric inverse problems: theory and applications" by Maatoug Hassine (15 - Numerical Analysis and Scientific Computing)

"Multi-Resolution Wavelet-Augmented Physics-Informed Neural Networks for Efficient and Accurate Solutions of Complex Financial Differential Equations" by Kavita Kavita (15 - Numerical Analysis and Scientific Computing)

"Local Optimization of Weak Distance Between Compact Surfaces on Special Euclidean Group" by Kazuki Koga (15 - Numerical Analysis and Scientific Computing)

"Lyapunov Stability Analysis of a Uncertain Linear System" by Vanel Lazcano (15 - Numerical Analysis and Scientific Computing)

"Inverse Problem for a Parabolic Equation" by Fagueye Ndiaye (15 - Numerical Analysis and Scientific Computing)

"Bridging Scales in Choanoflagellate Hydrodynamics: Hybrid Model of Small-Colony Behavior" by Hoa Nguyen (15 - Numerical Analysis and Scientific Computing)

"Numerical Integrators for Disordered Multidimensional Hamiltonian Systems" by Bob Senyange (15 - Numerical Analysis and Scientific Computing)

"Numerical Investigation of Two-Dimensional Two-Phase Kelvin-Helmholtz Instability Problem" by Abdullah Shah (15 - Numerical Analysis and Scientific Computing)

"Numerical Study of Waves Generated by Landslides in U-Shaped Bays" by Rani Sulvianuri (15 - Numerical Analysis and Scientific Computing)

"Novel iterative Algorithm for Solving Equilibrium Problem with Applications to Optimal Control and 3D Image Processing" by Victor Uzor (15 - Numerical Analysis and Scientific Computing)

"A Semi-Discrete Lagrangian-Eulerian Scheme for Systems of 3D Hyperbolic Conservation Laws in Cubic Grids" by Pedro Henrique Valerio de Godoi (15 - Numerical Analysis and Scientific Computing)

"Total Controllability for Fractional Differential Systems with Impulsive Effects" by Rajesh Dhayal (16 - Control Theory and Optimization)

"Stabilization of Unstable Periodic Orbits via Delayed Feedback Controls" by Dohan Kim (16 - Control Theory and Optimization)

"FIRST-ORDER ALGORITHMS FOR STOCHASTIC MULTI-OBJECTIVE OPTIMIZATION PROBLEMS" by Yiyang Li (16 - Control Theory and Optimization)

"Modified Gradient Descent Methods for Coupled-Constrained Minimization and Quasi-Variational Inequalities" by Nevena Mijajlovic (16 - Control Theory and Optimization)

"Negative Stepsizes Make Gradient-Descent-Ascent Converge" by Henry Shugart (16 - Control Theory and Optimization)

"Solution Theory for Singular Linear Switched Systems in Discrete Time" by Sutrisno Sutrisno (16 - Control Theory and Optimization)

"Dimension, Dynamics, and Comparison in C*-Algebras" by M. Ali Asadi-Vasfi (9 - Dynamics)

4:00 PM – 4:45 PM 122-AB Section Lecture

Probabilistic Models for Galois Groups

A fundamental object in number theory is the absolute Galois group of a number field, that is, the Galois group of the maximum algebraic extension. However, it is difficult to understand the structure of this group. Even smaller quotients of it, like the ideal class group, which is known to equal the Galois group of the maximum abelian unramified extension, can be difficult to describe. The Cohen-Lenstra program, beginning with work of Cohen and Lenstra and continued by many others, aims to describe the class group in a conjectural, probabilistic way: For a suitable notion of a random number field, calculate the probability distribution of the class group of a random number field as a distribution on the set of isomorphism classes of finite abelian groups. The non-abelian Cohen-Lenstra program aims to generalize this to other natural quotients of the absolute Galois group. I will discuss some progress in the non-abelian Cohen-Lenstra program and what it tells us about Galois groups.
4:00 PM – 4:45 PM 120-AB Section Lecture

Stability Problems in Collisionless Kinetic Theory

The Vlasov-Poisson system is the simplest non-collisional kinetic model. It describes the evolution of a distribution of particles influenced only by a force induced by their mean-field. We survey recent advances in the stability of stationary states and the asymptotic behavior of solutions for various variants of this system.
4:00 PM – 4:45 PM 121-AB Section Lecture

Stability Theory for Minimal Surfaces in Higher Codimension

There is a well-established theory of stable minimal hypersurfaces---i.e. minimal submanifolds in codimension one. In contrast, the theory in higher codimension is much less understood. This talk will discuss recent progress toward a stability theory for minimal surfaces in higher codimension.
4:00 PM – 4:45 PM 116-A Section Lecture

The Lens of Abelian Embeddings

We discuss a recent line of research investigating inverse theorems with respect to general k-wise correlations, and explain how such correlations arise in different contexts in mathematics. We outline some of the results that were established and their applications in discrete mathematics and theoretical computer science.
4:30 PM – 5:00 PM Benjamin Franklin Stage Art & Music @ ICM

Math, Music and the Mind: Analysis of the Performed Trio Sonatas of J. S. Bach

The music of J. S. Bach has influenced composers more than that of perhaps any other figure. His Trio Sonatas, in particular, offer some of the clearest insights into his pedagogy and have challenged generations of organists. For these reasons, they may also provide a uniquely powerful window into the structure of Bach’s music, and even into tonal music more broadly.

This talk will describe a collaborative project with the University of Michigan Organ Department to create high-precision digital recordings of these works, performed by students and faculty at varying skill levels. Using these digitization’s, together with direct representations of the musical scores, we investigate how music may be encoded in the mind.

Results challenge prevailing mathematical theories of music representation and reveal unexpected structural patterns in Bach’s compositions that invite further exploration. We also show how mathematical models of auditory processing in the brain can suggest new principles of musical composition.

Please note, as part of this experience, there will be an organ performance at Cathedral Basilica following the session (5:30 PM - 6:30 PM).

Click here to learn more about this session. 

5:00 PM – 5:45 PM 115-C

Between Figures and Symbols

The words figure and symbol are frequently employed to describe features of mathematical texts. However, what counts as a figure or a symbol within mathematics is unstable over time, place, individual, and research domain. This talk documents the value of this plasticity in the work of the geometer Charlotte Angas Scott and her students at the turn of the twentieth century.

5:00 PM – 5:45 PM 120-AB Joint Section Lecture

From Disordered Systems to the Critical 2D Stochastic Heat Flow

We review our joint work on the scaling limits of disordered systems, linking the notion of disorder relevance/irrelevance to that of sub/super criticality of singular SPDEs. This line of research culminated in the construction of the critical 2D Stochastic Heat Flow (SHF), a universal process which provides a non-trivial solution to the Stochastic Heat Equation in dimension 2 - a critical singular SPDE that lies beyond the reach of existing solution theories. The SHF also offers a rare example of a non-Gaussian scaling limit for a disordered system at its phase transition point in the critical dimension.
5:00 PM – 5:45 PM 115-B Section Lecture

Imaging, Inverse Problems, and AI: Where Does the Mathematics Go?

Mathematical imaging has long been a driver of fundamental developments across the mathematical sciences, rooted in the challenge of reconstructing and interpreting information from incomplete, noisy, or indirect data. This has led to deep connections with analysis, geometry, inverse problems, and probability, and has enabled transformative applications across science and engineering.

The rapid rise of artificial intelligence is now reshaping this landscape. Data-driven methods, in particular deep learning, achieve remarkable empirical performance in imaging tasks, yet they also raise fundamental questions about stability, generalisation, interpretability, and the role of prior knowledge and physical structure.

In this talk, I will argue that the central challenge is not to replace mathematical models with data, but to understand how data and structure interact. I will highlight recent developments that combine learning with geometry, physics, and variational principles, leading to new analytical frameworks and computational paradigms. From this perspective, imaging continues to act as a catalyst for mathematics—offering a fertile ground for developing the next generation of ideas at the interface of analysis, computation, and learning.

5:00 PM – 6:30 PM 121-C IMU Panel

Mathematics Research Institute Directors Meeting (Invitation Only)

By invitation only. 

5:00 PM – 5:45 PM 118-AB Section Lecture

Measure Evolution Equations for Multi-Agent Systems

Motivated by applications, several mathematical approaches have been proposed for the dynamics of large groups of intelligent agents. A typical example is vehicular traffic, where drivers make decisions and alter the energy of the system. A recent approach was developed by generalizing ordinary differential equations to measures, replacing vector fields with maps from probability measures on a manifold to probability measures on its tangent bundle. The new equations are called measure differential equations and allow for a multiscale representation of the physical system. A general theory, including existence and uniqueness results, generalization to multifunctions, and application to relaxed controls, is achieved using typical tools of optimal transport, such as the Wasserstein distance and its generalizations. While the existence of (weak) solutions is achieved under general assumptions, uniqueness is based on nonlinear functionals and on the concept of Dirac germ, which defines small-time evolution for finite sums of Dirac deltas. Circling back to applications, a general optimal control problem is formulated for the control of a large group via a small number of agents, also called Lagrangian controls. Mathematically, using the mean-field limit, one defines coupled systems of controlled ordinary differential equations and measure differential equations. The cost functionals include running costs defined in terms of (generalized) Wasserstein distance between the empirical measure of the controlled agents and the measure describing the uncontrolled ones, which elude classical tools. A list of open problems for future investigations is included.
5:00 PM – 5:45 PM 115-A Joint Section Lecture

Potent Categorical Representations

Classical harmonic analysis describes the decomposition of vector spaces of functions under the action of symmetries. In recent decades, a rich categorical harmonic analysis has emerged in which vector spaces of functions are replaced by categories of sheaves. We will explore some recent developments in this theory, centered around the search for a Fourier self-dual or symplectic form of categorical representation theory. This is inspired by the physics of 3d mirror symmetry, the representation theory of double affine Hecke algebras and genuine equivariance in algebraic topology.  The lecture is based on ongoing joint work with Germán Stefanich.

 

5:00 PM – 5:45 PM 116-A Section Lecture

Random Matrices, Intrinsic Freeness, and Sharp Non-Asymptotic Inequalities

Random matrix theory has played a major role in several areas of pure and applied mathematics, as well as statistics, physics, and computer science. This lecture aims to describe the intrinsic freeness phenomenon and how it provides new easy-to-use sharp non-asymptotic bounds on the spectrum of general random matrices.We will also present a couple of illustrative applications in high dimensional statistical inference.
5:00 PM – 5:45 PM 121-AB Section Lecture

Synthetic Perspectives on Higher Structures

Through painstaking work, higher structures, such as weak infinite-dimensional categories, can be built "analytically" out of sets. Elaborate formalisms have been developed to ensure that constructions involving these objects are equivalence-invariant. We present an alternate approach using domain-specific formal languages to work with higher structures "synthetically." We argue such formal systems make definitions, theorems, and proofs both easier to understand and easier to formalize. Our contributions to the synthetic theory of higher categories were developed over the course of joint work with Dominic Verity, Mike Shulman, Evan Cavallo, and Christian Sattler, among others.
5:00 PM – 5:45 PM 119-AB Section Lecture

The Geometry of Polynomials for Log-Concavity and Expansion

Log concavity is an important feature of many functions and discrete sequences appearing across mathematics, including combinatorics, algebraic geometry, convex analysis, and optimization. In this talk I will survey recent developments in our understanding of functional log concavity with a focus on applications to combinatorial inequalities and algorithms for approximate counting and sampling. At the heart of this story are rich classes of multivariate generating polynomials that give rise to discrete probability distributions that can be approximately sampled efficiently using Markov chains. The basis-generating polynomial of a matroid is a fundamental example. We will explore applications to matroids and extensions to other combinatorial structures. 

5:00 PM – 5:45 PM 122-AB Joint Section Lecture

The Intrinsic Approach to Moduli Theory

Moduli theory has captured the imagination of algebraic geometers for at least two centuries.  Up until the end of the 20th century, moduli spaces were constructed and studied by rigidifying the moduli problem using extrinsic data and applying geometric invariant theory. Over the last several decades, there has been a paradigm shift toward studying moduli problems intrinsically using the language of algebraic stacks.  We highlight recent advances in this direction that have incorporated ideas from geometric invariant theory to develop a structure theory for algebraic stacks. In the ideal situation, it allows one to decompose an algebraic stack into simpler strata and construct moduli spaces corresponding to each stratum. In addition to surveying some previous applications of the theory, we take a forward-looking perspective on the field and identify questions for future research.

5:00 PM – 5:45 PM 118-C Joint Section Lecture

The Method of Commuting Flows

We describe the recent progress on the well-posedness problem for completely integrable Hamiltonian PDE that has been made possible by the introduction of the method of commuting flows.
5:30 PM – 6:30 PM Cathedral Basillica (offsite) Art & Music @ ICM

Math, Music and the Mind: Organ Performance at Cathedral Basilica

6:00 PM – 6:45 PM 119-AB Section Lecture

A Combinatorial Ride from Macdonald Polynomials to Schubert Calculus and Back

When I started my Ph.D., I had never even heard of combinatorics. Adriano Garsia and Jeff Remmel eagerly stepped in and taught me that it is the study of a remarkable family of symmetric functions called Macdonald polynomials. By the time I discovered that their definition was not universally accepted, I had already been thoroughly indoctrinated. In this talk, I will share the Garsia–Remmel lessons, along with the story of how decades of playing with Young tableaux led to the development of a combinatorial architecture that underlies both these Macdonald polynomials and a branch of algebraic geometry known as Schubert calculus.
6:00 PM – 6:45 PM 122-AB Section Lecture

Algebraic Groups of Birational Maps

I will present some of the recent developments on algebraic groups acting via birational maps on algebraic varieties.
6:00 PM – 6:45 PM 118-C Joint Section Lecture

Coarse-Graining, Homogenization and Anomalous Diffusion

Many models in mathematical physics have detailed microscopic descriptions, yet their large-scale behavior is governed by only a few parameters. We describe a coarse-graining approach for divergence-form elliptic operators that replaces the microscopic coefficient field by two coarse-grained matrices attached to each spatial block. Analytically, the advantage is closure: data on a larger block are controlled by the same kind of data on smaller sub-blocks, enabling a scale-by-scale induction. Quantitative information passes from small to large scales through a new scale-local notion of ellipticity and corresponding coarse-grained versions of classical elliptic estimates. We illustrate the method in two settings. In high-contrast random media, we give a new estimate of the length scale at which homogenization sets in as a function of the ellipticity contrast of the coefficient field. In a second example, we consider the long-time behavior of diffusion processes advected by critically-correlated, incompressible drifts and prove superdiffusive behavior, in line with physics predictions. Taken together, these examples show that our scale-local notion of ellipticity is genuinely iterable across arbitrarily many scales and can make renormalization group-style arguments rigorous. This talk is joint with Tuomo Kuusi (University of Helsinki).
6:00 PM – 6:45 PM 118-AB Section Lecture

Conic Optimization for Extremal Geometry

The aim of this lecture is to highlight recent progress in using conic optimization methods to study geometric packing problems. We will look at four geometric packing problems of different kinds: two on the unit sphere-the kissing number problem and measurable \(\pi/2\)-avoiding sets-and two in Euclidean space---the sphere packing problem and measurable one-avoiding sets.
6:00 PM – 6:45 PM 120-AB Joint Section Lecture

Liouville Quantum Gravity: from Random Planar Maps to Conformal Field Theory

Originating in theoretical physics, Liouville quantum gravity (LQG) has been an important topic in probability  theory and mathematical physics in the past two decades. In this talk, we review two aspects of this topic. The first is that LQG describes the random conformal geometry of the scaling limit of random planar maps. We highlight the convergence of random planar maps under discrete conformal embedding, where couplings between LQG and the Schramm-Loewner evolution (SLE) play a key role. The second aspect is the connection to conformal field theory (CFT). Here we highlight the interplay between Liouville CFT and the SLE/LQG coupling, the CFT description of 2D quantum gravity coupled with conformal matter, and applications to SLE and 2D statistical physics.
6:00 PM – 6:45 PM 115-B Section Lecture

Predictive Inference and Inverse Probability

We consider the construction of prior-free posterior distributions for parameters of interest based on one-step-ahead predictive distribution functions. This contrasts both Bayesian and Frequentist approaches, which derive inference through likelihood functions defined on the observed data. In our formulation, the observed data are not modelled directly; instead, predictive models are developed for the unobserved population data relevant to the inferential target. Predictive models are then used to sample complete data sets from which posterior inference may be obtained for any statistic of interest.
6:00 PM – 6:45 PM 115-A Joint Section Lecture

Representations of Reductive Algebraic Groups in Positive Characteristic

We will survey some recent results regarding representations of reductive algebraic groups over algebraically closed fields of positive characteristic. In particular, we will explain a character formula for indecomposable tilting modules, and some progress towards a conjecture of Humphreys on cohomological support of these modules. (Joint lecture with P. Achar.)
6:00 PM – 6:45 PM 116-A Section Lecture

Statistical and Computational Challenges in Ranking

Ranking problems are prevalent in modern statistical, machine learning, and computer science literature. This includes a variety of practical situations ranging from ranking experts/workers in crowd-sourced data, ranking players in a tournament or equivalently sorting objects based on pairwise comparisons. A main challenge in this field is to construct an estimator of the rank of the experts, based on incomplete and noisy data. In this talk, we focus on understanding the problem of ranking both from an informational and a computational perspective. Namely, we want to characterize the fundamental statistical thresholds for optimal estimation over all possible estimators, but also to characterise the fundamental thresholds for computationally efficient estimation, restricted to polynomial-time estimators. A core question for these problems is on whether statistical optimality is compatible with computational efficiency.To do that, we first consider the simpler sub-problem of sub-matrix detection and estimation, which is useful to apprehend the more complex problem of ranking - and we will particularly focus on computational lower bounds. Based on results for this problem, we explain how they can be used to solve the more challenging problem of ranking.
6:00 PM – 6:45 PM 121-AB Section Lecture

Symplectic Weyl Laws

We survey a number of formulas that have recently been established in low-dimensional symplectic geometry that are analogous to Weyl's Law for the Laplace spectrum. We discuss applications to problems in dynamics and problems about the algebraic structure of certain groups of homeomorphisms of surfaces. We state some open questions related to the subleading asymptotics.
7:15 PM – 8:15 PM Terrace Ballroom Public Lecture

Mathematics in the Age of AI

Current AI tools, when combined with formal verification and modern collaboration platforms, are enabling new ways to do mathematics at scale, with increasingly broad collaborations between professional mathematicians, other scientists, members of the public, and AI tools.  Yet these tools continue to have only a modest impact on more traditional mathematical objectives, such as making progress on individual highly difficult problems.  In this lecture we survey the recent achievements of these new paradigms, as well as their continuing limitations.

Saturday, July 25, 2026

9:00 AM – 6:00 PM Hall E - Expo Expo and Collaborations

Exhibition & Collaboration

9:00 AM – 10:00 AM Terrace Ballroom Plenary Lecture

Randomness, Rotations and Resonances

I will discuss several problems on the interface of probability and number theory there a recent progress came from the understanding of the geometry of resonances.

10:15 AM – 11:15 AM Terrace Ballroom Plenary Lecture

Learning and the Price of Anarchy in Games

We investigate repeated strategic interactions where participants use learning algorithms to guide their decisions. As machine learning increasingly powers online systems—from traffic and packet routing to ad auctions—it becomes essential to understand how strategic behavior affects performance, and how to design systems that ensure robust outcomes.Over the past two decades, researchers have developed powerful tools to quantify the inefficiency caused by selfish behavior, known as the Price of Anarchy. Foundational results show that when participants use learning algorithms satisfying the no-regret condition, the resulting inefficiency remains bounded—even in repeated games. However, these analyses typically assume that each round is independent, with no carryover effects from previous outcomes.In reality, many systems exhibit an evolving dynamic state. We explore such dynamic games, where outcomes in one round directly influence future interactions. We will highlight ongoing research studying this phenomenon in the context of a game modeling queuing system: routers compete for servers, and packets that fail to get served must be resent. This creates a feedback loop where the number of packets in each round depends on prior success, resulting in a highly dependent random process. We study how much excess server capacity is needed to guarantee system stability, even when participants behave selfishly and myopically.
10:30 AM – 10:50 AM 120-AB Short Communications

A Result on the Jacobian Conjecture

The Jacobian conjecture has been launched by O. Keller in 1939 and is still open until now, saying that a polynomial function $G$ from $\mathbb{R}^n$ to itself for $n\geq2$ having jacobian $det\left(J_G\right)$ equal to 1, is bijective. It is the 16th on the Smale's list of problems for the 21st century. We solve partially it when $n=2$ on the coordinate system $(x,y)$ with $G=(G_1,G_2)$ when $$G_1:=a_0+a_1x+l_1y+\sum^m_{i=1}b_ixy^i+\sum^m_{i=1}e_ix^2y^i+\sum^m_{i=2}c_iy^i+\sum^m_{i=2}f_ix^i$$$$G_2:=a_{-1}+r_1x+s_1y+\sum^m_{i=1}k_ixy^i+\sum^m_{i=1}w_ix^2y^i+\sum^m_{i=2}t_iy^i+\sum^m_{i=2}u_ix^i,$$where all coefficients of the polynomials are real. We define the degree of $G$ as $deg(G)=m$ for $m\geq2$ and solve $det\left(J_G\right)=1$ by Maple: First, for $f_i=u_i=e_i=w_i=0$ for all $2\leq i\leq m$ when $e_1=w_1=0$ by solving $det\left(J_G\right)=1$ for $deg(G)=2m$ when $f_i=u_i=e_i=w_i=0$ for all $2\leq i\leq 2m$, $e_1=w_1=0$ and $b_i=c_i=k_i=t_i=0$ for all $m+1\leq i\leq 2m$. Then, we find that $G$ is injective, then $G$ is a bijection. Second, when $e_i=w_i=0$ for all $1\leq i\leq m$, we have $f_i=u_i=0$ for all $3\leq i\leq m$. Then, we have three cases to be solved in Maple up to the symmetry on $(x,y)$: the first is the one above which has already been solved, the second is:$$G_1:=a_0+a_1x+l_1y+\sum^s_{i=2}c_iy^i$$$$G_2:=a_{-1}+r_1x+s_1y+\sum^s_{i=1}k_ixy^i+\sum^{2s}_{i=2}t_iy^i+\sum^2_{i=2}u_ix^i,$$and the last is:$$G_1:=a_0+a_1x+l_1y+\sum^{s}_{i=1}b_ixy^i+\sum^{2s}_{i=2}c_iy^i+\sum^2_{i=2}f_ix^i$$$$G_2:=a_{-1}+r_1x+s_1y+\sum^s_{i=1}k_ixy^i+\sum^{2s}_{i=2}t_iy^i+\sum^2_{i=2}u_ix^i$$ for $s\geq1$ and $2s\leq m$. Let us use the following theorem, $G$ beying polynomial, $G$ is proper if and only if $G$ hasn't zero in the infinity. We solve $G_1(x,y)=0$ and $G_2(x,y)=0$ as polynomials of second degree in $x$, looking for zeros of $G$ in the infinity by Maple. Thus, We find that $G$ is proper. $G$ beying a local homeomorphism and proper, by the Hadamard theorem on local homeomorphism, $G$ is bijective. Third, we solve $det\left(J_G\right)=1$ in general form and we have $e_i=w_i=0$ for all $2\leq i\leq m$, we run again the Maple program with this data when $e_1\neq0$ or $w_1\neq0$, we find that $deg(G)\leq4$. By Moh's result saying that if the usual degree of $G$ is less than 101, the Jacobian conjecture is true for $n=2$, we get $G$ as a bijection. We conclude by these results that $G$ verifies the Jacobian conjecture for $m\geq2$.
10:30 AM – 10:50 AM 118-AB Short Communications

Backward-Backward Splitting with Warped Yosida Regularization for Monotone Inclusions

In this talk, we introduce the notion of warped Yosida regularization and study the asymptotic behaviour of the trajectory of dynamical systems generated by warped Yosida regularization, which includes Douglas-Rachford dynamical system. We analyze an algorithm where the inclusion problem is first approximated by a regularized one and then the preconditioned regularization parameter is reduced to converge to a solution of the original problem. We propose and investigate backward-backward splitting using degenerate preconditioning for monotone inclusion problems. The applications provide a tool for finding a minima of a preconditioned regularization of the sum of two convex functions.
10:30 AM – 10:50 AM 115-A Short Communications

Frobenius, Separability and Maschke Properties for Contramodules Over Entwining Structures with Several Objects

A contramodule $N$ over a coalgebra $C$ consists of a structure map $Hom(C,N)\longrightarrow N$ satisfying certain conditions determined by coassociativity and counitality conditions. Although the notion of contramodules is classical, introduced by Eilenberg and Moore along with comodules, their development has somewhat lagged behind the study of comodules. However, in recent years, there has been much interest in developing the theory of contramodule categories in tandem with those of comodule and module categories.More specifically, we work with contramodule categories over an entwining structure. An entwining structure $(C,A,\psi)$ consists of a coalgebra $C$ and an algebra $A$ woven together with a map $\psi:C\otimes A\longrightarrow A\otimes C$ that satisfies conditions similar to a bialgebra. For instance, an entwining structure captures the essenceof a coalgebra Galois extension, or may be seen as a noncommutative replacement for aprincipal fiber bundle produced by the quotient of the free action of an affine algebraicgroup on a scheme. The properties of such a noncommutative space are then understoodin terms of the category of modules over it. In general, modulesover an entwining structure bring together several objects of studyin the literature, such as relative Hopf modules, Doi-Hopf modules and Yetter-Drinfeldmodules. We consider contramodules over an entwining structure $(\mathscr C,A,\psi)$, where $\mathscr C$ is a ``coalgebra with several objects,'' i.e., a category like object with cocomposition structures. This is the coalgebra counterpart of the philosophy of Mitchell, where a small preadditive category is seen as a ``ring with several objects.'' The entwined contramodules now capture essential properties of the noncommutative quotient space associated to $(\mathscr C,A,\psi)$. In fact, this noncommutative quotient space need not exist as an explicit geometric object, but is understood only by means of the modules, comodules and contramodules over it. As such, we use adjoint functors between these contramodule categories to study ring like properties of extensions between these noncommutative quotient spaces. In particular, we give explicit categorical criteria for these extensions to satisfy (1) Frobenius properties, (2) Mashcke properties and (3) separability properties.
10:30 AM – 10:50 AM 119-AB Short Communications

K-Type Dynamics of $\mathbb{Z}^d-$actions

Classical discrete-time dynamical systems are actions of the group $\mathbb{Z}$, where the total order of time allows one to study asymptotic behavior through limits as $n \to \infty$. A generalization is to consider actions of $\mathbb{Z}^d$ for $d \geq 2$. However, the absence of a total order in $\mathbb{Z}^d$ removes the notion of a unique forward direction, making it impossible to consider "$n \rightarrow \infty$". To address this, Oprocha in [Piotr Oprocha. “Chain recurrence in multidimensional time discrete dynamical systems”, Discrete and Continuous Dynamical Systems 20.4 (2007), pp. 1039-1056] introduced a partial order on elements of $\mathbb{Z}^d$. The key insight was that instead of a single total order, one can define multiple partial orders, each corresponding to a different ``direction" of progression. Each integer $k \in \{1, 2, \dots, 2^d\}$ corresponds to one of the $2^d$ orthants (or “quadrants”) in $\mathbb{Z}^d$, and the associated order $\ge^k$ defines a notion of positivity relative to that orthant. For example, in $\mathbb{Z}^2$, $k=1$ corresponds to the standard first quadrant ($n_1 \ge 0, n_2 \ge 0$), while $k=2$ corresponds to the second quadrant ($n_1 \le 0, n_2 \ge 0$), and so on.Based on this, we introduced and studied dynamical notions of $k-$type chaos and $k-$type topological entropy. We also formulated and proved the $k-$type von Neumann Ergodic Theorem. In this presentation, I will talk on all these notions and related results. All these works are jointly done by me and my doctoral student Mr. Anshid Aboobacker. The results on $k-$type chaos are published in [Anshid Aboobacker and Sharan Gopal. “$k$-type chaos of $\mathbb{Z}^d$-actions”. Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis, 32 (2025), pp. 139–153.]
10:30 AM – 10:50 AM 116-A Short Communications

Nonparametric Estimation of the Renewal Function on Mixing Random Fields

In queuing theory, the renewal function is considered in many papers and several researchers have contributed to this function. In this presentation, we study the nonparametric and asymptotically unbiased estimator of the renewal function based on mixing random fields indexed by $\mathbb{Z}^d$. Many applications can be founded such as the contamination of a contagious disease between individuals (people, animals or plants) on the Earth (dimension 2) or in the Oceans (dimension 3). It will spread faster between individuals depending on their proximity. The expectation of the average time for the first $k$ individuals to be affected by the disease before a time $t$ in a given region will depend generally of a certain mixing law. The estimator is constructed from the separation method of $\mathbb{Z}^d$ with which we obtain weakly dependent blocks of random fields. It consists to separate this domain into collection of disjointed blocks alternately of large size and small size. We focus on the almost sure convergence and asymptotic normality of the renewal function estimator based on stationary, ergodic and strongly mixing random fields.
10:30 AM – 10:50 AM 118-C Short Communications

Nonuniqueness of (1 + Alpha)-Hölder Continuous Isometric Embeddings Between Contact Manifolds

Isometric embeddings between a domain manifold and a target manifold are differentiable maps $f$ such that the pullback of the target metric $h$ coincides with the metric $g$ in the domain manifold. This problem can also be formulated as a non-linear PDE via $\nabla f^{\top}h\nabla f = g$. In the case of contact manifolds, it is additionally required that the embedding preserves a certain restriction on the tangent bundle.We prove that the Nash iteration scheme can be quantified in order to construct infinitely many $C^{1,\alpha}$ isometric embeddings for contact manifolds. In this way, we extend existing results by D'Ambra regarding non-uniqueness for $C^{1}$ regularity. The strategy of the proof follows a paper by Conti, De Lellis and Székelyhidi Jr. on the Riemannian case. The main difficulty in the context of contact manifolds is to keep the additional linear constraint coming from the contact setting along the iteration procedure.In the larger program of a quantitative analysis of isometric embeddings between sub-Riemannian manifolds, our result can be seen as an important first step. Another aspect is the flexibility of this convex integration method: the geometric constraint coming from the contact condition is just one special case of a (potentially large) class of admissible constraints, under which this scheme can still be applied.This is joint work with László Székelyhidi Jr.
10:30 AM – 10:50 AM 115-C Short Communications

Rubin-Stark Units and Equivariant Annihilators of Class Groups

We establish a Gras-type equality for finite abelian extensions of number fields, relating Fitting ideals of certain components of ray class groups to annihilators of quotients involving Rubin-Stark elements. This framework connects special values of Artin $L$-functions at $s=0$ with the arithmetic of class groups and units for general rank $r$. We show that the equality is equivalent to the corresponding component of the equivariant Tamagawa Number Conjecture, and we discuss its consequences in the cases $r=0$ and $r=1$, which recover and refine results related to the Brumer-Stark conjecture and certain index formulae involving elliptic units.
10:30 AM – 10:50 AM 115-B Short Communications

Stochastic Currents of Fractional Brownian Motion: Existence and Regularity

By using white noise analysis, we study the integral kernel $\xi(x)$, $x\in\mathbb{R}^{d}$, of stochastic currents corresponding to fractional Brownian motion with Hurst parameter $H\in(0,1)$. For $x\in\mathbb{R}^{d}\backslash\{0\}$ and $d\ge1$ we show that the kernel $\xi(x)$ is well-defined as a Hida distribution for all $H\in(0,1)$. For $x=0$ and $d=1$, $\xi(0)$ is a Hida distribution for all $H\in(0,1)$. For $d\ge2$, then $\xi(0)$ is a Hida distribution only for $H\in(0,1/d)$. For $d=1$, $x \neq 0$, and $H \in (0,1)$, we show that $\xi(x) \in \mathcal{G}'$, the space of regular generalized functions. Elements of the space $\mathcal{G}'$ and elements from the negative Sobolev-Watanabe distribution spaces share the property that partial sums of their chaos decomposition are square integrable functions. More precisely, we show that $\xi(x) \in \mathcal{G}_{-s} \subset \mathcal{G}'$ for $x \neq 0$, $H \in (0,1)$, and all $s > 0$.
10:50 AM – 11:10 AM 119-AB Short Communications

Anisotropic Techniques Beyond Smooth Dynamics: The Bilateral Shift Case

Joint work with Mateus Marra (ICMC-USP). We introduce anisotropic Banach spaces of distributions adapted to the bilateral shift over a finite alphabet. On these spaces, the associated transfer operator is shown to be quasicompact with a spectral gap, and its $1$--eigenspace is spanned by the Gibbs state corresponding to some given potential. This functional-analytic framework allows us to establish exponential decay of correlations not only for H\"older observables, but also for a broad class of highly irregular measures and distributions, including measures supported on graphs of H\"older functions. Our results show that anisotropic techniques remain effective well beyond the smooth setting, providing new tools for symbolic and non-smoothdynamical systems.
10:50 AM – 11:10 AM 118-C Short Communications

Ball Separation Characterization of Ball Dentability and Related Properties

In Euclidean spaces, every closed, bounded, convex set can be characterized by two equivalent notions of separation properties. This is not true in general for arbitrary Banach spaces. In this work, we present a ball separation characterization for spaces where the unit ball is dentable. We also explore related properties.
10:50 AM – 11:10 AM 115-C Short Communications

Equivariant Birational Geometry

Let $X$ be an algebraic variety and $G$ a finite subgroup of the automorphism group of $X$. We will discuss a few results on how rationality properties of $X$ behave under the $G$-actions.
10:50 AM – 11:10 AM 116-A Short Communications

Hierarchical Quasi-Cyclic Codes from Reed-Solomon and Polynomial Evaluation Codes

In this communication, we introduce a family of algebraically constructed hierarchical quasi-cyclic codes. These codes are built from Reed-Solomon and polynomial evaluation codes using a 1964 construction of superimposed codes by Kautz and Singleton. Using a novel ordering of the codewords and evaluation points, we show both the number of levels in the hierarchy and the index of these q-ary-derived codes are determined by the field size. We compute explicit code parameters and properties as well as some additional bounds on parameters such as rank and distance. In particular, starting with Reed-Solomon codes of dimension two yields hierarchical quasi-cyclic codes with Tanner graphs of girth 6. Finally, we present a table of small code parameters and note that some of these codes meet the best known minimum distance for binary codes, with the additional hierarchical quasi-cyclic structure.
10:50 AM – 11:10 AM 115-A Short Communications

Linearity Index in the Interval of Matching Numbers

The linearity index of an edge ideal $I(G)$, is the smallest integer $k$ such that the $k$th squarefree power of $I(G)$ has linear resolution. It is known that the linearity index is bounded between the induced matching number and the matching number of the graph. In this talk, we will discuss the possible values of the linearity index in the interval of matching numbers. This is based on joint work with Takayuki Hibi.
10:50 AM – 11:10 AM 115-B Short Communications

Multiscale Random Matrices and Scale Invariance in High Dimensions

Scale invariance is a striking property that emerges from scaling limits or the renormalization of many stochastic systems (cf. fractional Brownian motion, the critical Ising model, etc.). Scale invariance -- and related notions of universality -- are cutting-edge topics in the study of stochastic systems with several degrees of freedom, i.e., in high-dimensional probability theory. Furthermore, research on high-dimensional scale invariance impacts several fields of statistical application, including neuroscience, network traffic and machine learning, owing to its inherent connection with large data sets. In this talk, we show that the recently proposed framework of multiscale random matrices -- particularly, wavelet random matrices -- provides a natural renormalization-type setting for the study of high-dimensional, scale-invariant (fractal) dynamics.
10:50 AM – 11:10 AM 118-AB Short Communications

On the Numerical Implementation for Solving Impulsive Differential Equations with Loadings

We consider the following linear problem for impulsive differential equations with loadings:$$ \frac{dy}{dt}=A_0(t)y + \sum \limits _{i=1}^m M_i(t) \lim \limits_{t\to \theta_i +0}\dot{y}(t) +\sum \limits _{i=1}^{m} A_i(t) \lim \limits_{t\to \theta_i +0}y(t) + f(t), \quad t\in (0,T), \eqno(1) $$$$ \sum \limits _{j=0}^{m+1} D_j y(\theta_j) =d, \quad d\in R^{n}, \quad y\in R^{n}, \eqno(2) $$$$B_i\lim \limits_{t\to \theta_i -0} y(t)-C_i\lim \limits_{t\to \theta_i +0} y(t)=\varphi_i, \quad \varphi_i\in R^{n}, \quad i=\overline{1,m},\eqno(3) $$where $(n \times n)$-matrices $A_j(t)$, $(j=\overline{0,m}),$ $M_i(t)$, $(i=\overline{1,m}),$ and $n$-vector-function $f(t)$ are piecewise continuous on $[0,T]$ with possible discontinuities of the first kind at the points $t=\theta_i,$ $(i=\overline{1,m})$. $D_j$, $(j=\overline{0,m+1}),$ $B_i$, and $C_i$, $(i=\overline{1,m})$ are constant $(n\times n)$ - matrices, and $\varphi_i,$ $(i=\overline{1,m})$ are constant $n$ vector functions, $0=\theta_0<\theta_1<\theta_2<\ldots<\theta_{m-1}<\theta_m<\theta_{m+1}=T$.The aim of this paper is to develop and investigate an efficient numerical method for solving a multipoint boundary value problem for impulsive differential equations with loadings (1)--(3). The proposed technique is based on the Dzhumabaev parametrization method, which enables the transformation of the original boundary value problem into a system of algebraic equations combined with a set of Cauchy problems. Such a reformulation substantially simplifies the numerical realization of the problem, reduces computational complexity, and provides a convenient framework for constructing accurate approximate solutions. Moreover, the resulting approach allows for flexible implementation and can be effectively applied to a wide class of impulsive differential equations with multipoint boundary conditions.
10:50 AM – 11:10 AM 120-AB Short Communications

ω-Bach Solitons and Quasi-Bach Solitons on Some Riemannian Manifolds

In this article, we introduce $\omega$-Bach tensor corresponding to one form $\omega$ and correspondingly introduce $\omega$-Bach solitons and almost $\omega$-Bach solitons. We characterize almost $\omega$-Bach solitons, when the potential vector field of the soliton generates an infinitesimal harmonic transformation, or is an affine conformal vector field, or is a projective vector field, or is a Killing vector field, when the $\omega$-Bach tensor is divergence free, or is a harmonic 1 form or is a Killing 1-form. One of the main results of this note is that we explicitly find some of the gradient almost $\omega$-Bach solitons on the product manifolds $S^2\times H^2$, $R^2\times H^2$ and $R^2\times S^2$. We have also introduced quasi-Bach tensor and correspondingly introduced almost quasi Bach solitons. We explore some properties of gradient quasi Bach solitons with harmonic Weyl curvature tensor. We also find the evolution of volume, Einstein metric, Ricci curvature and scalar curvature, under the quasi Bach flow. Our results obtained here extends the results of Bach solitons and Bach flow. Finally, we obtain the characterization of gradient quasi-Bach soliton of type I, a particular quasi Bach soliton, on the product manifolds $S^2\times H^2$ and $R^2\times H^2$.
11:00 AM – 12:45 PM Benjamin Franklin Stage Films @ ICM

Journeys of Black Mathematicians: Creating Pathways

Film Directed by George Csicsery

Journeys of Black Mathematicians: Creating Pathways is the second installment of a two-part documentary series which reflects the mathematical excellence of contemporary Black mathematicians. Featuring over 50 individuals representing a panoramic view of greatness in mathematics and STEM, these films seek to inspire today’s Black and minority graduate and college students as well as K-12 children across the USA and around the world who are developing the confidence that they too can become stellar mathematicians and STEM researchers.

Panelists

  • Dawn Lott, Delaware State University
  • Nathaniel Whitaker, University of Massachusetts
  • Sylvester James Gates, Jr., University of Maryland
  • Moderators: Johnny Houston and Aris Winger
11:10 AM – 11:30 AM 118-AB Short Communications

A Method for Solving a Multipoint Boundary Value Problem with a Nonlinear Integro-Differential Operator

The study is focused the applicability of Dzhumabaev parametrization method to multipoint boundary value problems for the Duffing-type integro-differential operator equation:$$\frac{d^2x}{dt^2}+\alpha \frac{dx}{dt}+\beta x^3 + \gamma x^5 = \eta cos(\omega t)+ \varphi_1(t)\int\limits_{0}^{T}\psi_1(\tau)x(\tau)d\tau+\varphi_2(t)\int\limits_{0}^{T}\psi_2(\tau)\frac{\partial x(\tau)}{\partial \tau}d\tau+p(t), \, t\in (0, T), $$$$\sum\limits_{j=0}^{N} b_{ij} x(t_j)+\sum\limits_{j=0}^{N} c_{ij} \left.\frac{\partial x}{\partial t}\right|_{t=t_j}+g_i\bigg(\left.x(t_0),\ldots, x(t_N),\frac{\partial x}{\partial t}\right|_{t=t_0},\ldots, \left.\frac{\partial x}{\partial t}\right|_{t=t_N}\bigg)=d_i, \, i=1,2,$$where $x$ is displacement; $\alpha,$ $\beta,$ $\gamma,$ $\eta,$ $\omega$ are arbitrary constants; and $\varphi_k(t),$ $\psi_k(\tau),$ $k=1, 2,$ and $p(t)$ are continuous on $[0,T],$ $b_{ij},$ $c_{ij}$ are given numbers, $g_i:R^{2(N+1)} \rightarrow R$ is continuous.The original problem is reformulated as an equivalent parametric multipoint problem, which was then decomposed into two subproblems: a nonlinear special Cauchy problem and a system of nonlinear algebraic equations. The special Cauchy problem is addressed via linearization at fixed parameter values and solved through a sequence of stepwise linear approximations. The solutions obtained are subsequently employed to construct the right-hand side of the algebraic system and its associated Jacobi matrix. On this basis, a new approach for solving the original problem is developed. The efficiency and convergence of the proposed approach were confirmed through a numerical examples.
11:10 AM – 11:30 AM 120-AB Short Communications

Convergence of Riemannian Manifolds and Metric Spaces

We present advances in the study of Gromov-Hausdorff (GH) and Sormani-Wenger Intrinsic Flat (SWIF) Convergence of Riemannian manifolds, metric spaces, and integral current spaces. We begin with a review of GH and F convergence including Gromov’s GH Compactness Theorem and Wenger’s SWIF Compactness Theorem. We also review volume preserving notions of convergence including work of Fukaya, Cheeger, Colding, Naber, Sturm, Portegies, Matveev, Jauregui, Lee and Perales. We compare and contrast these notions using examples from joint papers with Allen and by Allen-Bryden. We present methods of proving convergence from joint work with Lakzian, joint work with Huang and Lee, the joint VADB paper with Allen and Perales, and the recent monotone convergence paper with Perales. We present applications of these methods to study sequences of manifolds with nonnegative scalar curvature. This includes tunnel constructions with Basilio and Dodziuk, with Basilio and Kazaras, and by Sweeney and Krandel. We conclude with the extreme limits of manifolds with nonnegative scalar curvature in work with Tian and Wang and with Tian and Yeung.
11:10 AM – 11:30 AM 119-AB Short Communications

Linear Stability of Viscoelastic Sub-Diffusive Plane Poiseuille Flow Under a Transverse Magnetic Field

This study examines the linear stability and flow behavior of a viscoelastic, sub-diffusive plane Poiseuille flow in the presence of an external magnetic field. Viscoelastic effects are modeled using the fractional upper-convected Maxwell (FUCM) model. Neutral stabilitycurves are obtained for different values of the sub-diffusive exponent, Reynolds number, elasticity, magnetic field strength, and viscosity ratio. The results show that changing the order of the sub-diffusive exponent significantly shifts the most unstable flow mode. Tosupport the linear stability findings, direct numerical simulations are also performed. The evolution of the polymer conformation tensor, which remains symmetric and positive definite, is studied using a Riemannian metric and characterized through its three scalarinvariants. Overall, the results provide new insights into the dynamics of complex viscoelastic flows and may be useful for practical applications in engineering and related scientific fields.
11:10 AM – 11:30 AM 115-B Short Communications

Non-Split, Alternating Links Bound Unique Seifert Surfaces in the 4-ball

We show that any two same-genus, oriented, boundary parallel surfaces bounded by a non-split, alternating link into the 4-ball are smoothly isotopic fixing boundary. In other words, any same-genus Seifert surfaces for a non-split, alternating link become smoothly isotopic fixing boundary once their interiors are pushed into the 4-ball. We conclude that a smooth surface in $S^4$ obtained by gluing two Seifert surfaces for a non-split alternating link is always smoothly unknotted.
11:10 AM – 11:30 AM 118-C Short Communications

Norm Behavior of Jordan and Bidiagonal Matrices

According to the spectral theorem, the norm behavior of normal matrices can be completely determined from their spectrum; however, for non-normal matrices, the spectrum alone is not sufficient to describe their behavior. Determining the norm behavior of non-normal matrices from spectral-related sets is a fundamental problem in matrix theory. In this work, we prove that the pseudospectra and condition spectra completely characterize the norm behavior of Jordan matrices for any matrix $p$-norm. Furthermore, we provide sufficient conditions for determining the $1$-norm and $\infty$-norm behavior of bidiagonal matrices based on their pseudospectra and condition spectra.
11:10 AM – 11:30 AM 116-A Short Communications

On the Orbit Membership Problem for Solvable Groups of Affine Transformations on a Finite Group

The constructive orbit membership problem for a permutation group acting on a set is defined as follows: given two elements (or points) of the set, determine one or all group elements that map the first point to the second. In this paper, we study this problem in the context of \textit{affine transformations}, which are compositions of automorphisms and translations of a group. We show that for a solvable group of affine transformations acting on a \textit{sufficiently preprocessed} finite group, the constructive orbit membership problem can be reduced, in randomized polynomial time, to instances of the discrete logarithm problem and the computation of multiplicative orders in finite fields. This special case of the constructive orbit membership problem captures several important computational problems that underlie the security of various cryptographic protocols, particularly in the domain of group-based cryptography. Notable examples include the semidirect discrete logarithm problem, the generalized discrete logarithm problem in arbitrary finite non-abelian groups, the automorphism search problem (the generalization of the conjugacy search problem), and the decomposition problem. Therefore, we also examine the implications of our results for the security of cryptographic protocols that rely on these underlying problems.
11:10 AM – 11:30 AM 115-A Short Communications

Structure-Preserving Transformations: Recent Updates on the Homological Analysis of Bieberbach Groups

Homological invariants are powerful algebraic tools that are used to capture and classify the structural properties of groups, particularly through their extensions and cohomology. These invariants provide deep insights into the algebraic configuration of symmetry and structure, making them highly relevant in various areas of mathematics and physics. In crystallography, the symmetrical arrangement of atoms in crystalline solids naturally leads to the study of groups that preserve these symmetries. Among such groups, Bieberbach groups—which are torsion-free, discrete, and cocompact subgroups of the isometry group of Euclidean space—play a central role in modelling the symmetry of crystal lattices. Their intricate algebraic structure allows for the application of homological methods to analyze and classify their properties. This talk will present recent developments in the homological analysis of Bieberbach groups, with a particular focus on the influence of their point groups, whether abelian or nonabelian. Special attention will be given to new results, techniques, and classification outcomes that contribute to the growing body of knowledge in this area.
11:10 AM – 11:30 AM 115-C Short Communications

The Reduced Special Fiber of Any Potentially Semistable Model of a Curve Is Semistable

We show that if $X$ is a smooth projective curve defined over a complete discretely valued field $K$ with algebraically closed residue field $k$, then any potentially semistable model of $X$ already has semistable reduced special fiber.
11:30 AM – 11:50 AM 118-AB Short Communications

A Meshfree RBF-FD Technique to Solve Fractional Schamel–KdV Equation for Ion-Acoustic Solitary Waves

The Schamel–KdV equation plays a vital role in studying the effect of electron trapping on the nonlinear interaction of ion-acoustic waves in plasma and dusty plasma. This work presents a numerical scheme-based radial basis function-finite difference (RBF-FD) method to solve the time-fractional Schamel–KdV equation. In the discretization process, a finite difference technique is used to discretize the temporal derivative, while the multiquadric RBF is used to approximate the spatial derivatives. The theoretical convergence and stability analysis of the time-discrete scheme are also established. Numerical experiments are executed through some illustrated problems, and the obtained results are compared with that acquired by the tanh method and Kudryashov method solutions to show the high accuracy and plausibility of the proposed technique. Also, the graphical representations are given to demonstrate the physical interpretation of the resulting wave structures.
11:30 AM – 11:50 AM 116-A Short Communications

Additive Group Codes and Duality on Group Algebras Over Chain Rings

Given a finite group $G$ and an extension of finite chain rings $S|R$, one can consider the group rings $\mathscr{S} = S[G]$ and $\mathscr{R} = R[G]$. The group ring $\mathscr{S}$ can be viewed as an $R$-bimodule, and any of its $R$-submodules naturally inherits an $R$-bimodule structure; in the framework of coding theory, these are called additive group codes, more precisely a (left) additive group code is a linear code which is the image of a (left) ideal of a group algebra via an isomorphism which maps $G$ to the standard basis of $S^n$, where $n=|G|$. We will show a symmetric, nondegenerate trace–Euclidean inner product on $\mathscr{S}$.Two additive group codes $\mathcal{C}$ and $\mathcal{D}$ form an {additive complementary pair} (ACP) if $\mathcal{C} + \mathcal{D} = \mathscr{S}$ and $\mathcal{C} \cap \mathcal{D} = \{0\}$. For two-sided ACPs, we prove that the orthogonal complement of one code under the trace–Euclidean duality is precisely the image of the other under an involutive anti-automorphism of $\mathscr{S}$, linking coding-theoretical ACPs with module orthogonal direct-sum decompositions, representation theory, and the structure of group algebras over finite chain rings.
11:30 AM – 11:50 AM 115-B Short Communications

An Optimal Eighth-Order Scheme for Nonlinear Equations with Known Multiplicity and Applications to Soil Nutrient Response, Hanging Object, and Kepler’s Equation

In recent years, considerable attention has been devoted to developing advanced iterative techniques for solving nonlinear equations with multiple roots of known multiplicity, particularly methods of higher order involving derivatives. However, constructing higher-order iterative schemes that are free from derivatives remains a challenging task, leaving a notable gap in the existing literature. To address this, we propose a novel three-step, eighth-order Traub-Steffensen-type iterative method that avoids derivatives by employing first-order divided differences. The second and third steps are further refined using weight functions of one and two variables, respectively, ensuring both accuracy and efficiency. The proposed scheme requires only four functional evaluations per iteration and achieves the optimal eighth-order convergence in accordance with the Kung-Traub conjecture, with an efficiency index of 1.6818. A rigorous convergence analysis confirms the theoretical order, while extensive numerical experiments performed using Mathematica 8, Maple 22, and MATLAB 2014a demonstrate the stability, accuracy, and superior performance of the scheme compared to existing eighth-order approaches. To establish its practical effectiveness, the method is applied to a range of real-world nonlinear problems with multiple roots, including the soil nutrient response model, the hanging object problem, kepler’s equation, eigenvalue problems, and various standard test functions. Comparative studies reveal significant improvements in computational order of convergence, residual error, and the difference between successive iterates. Furthermore, basins of attraction are analyzed to visualize the regions of convergence and to examine the sensitivity of the method to initial guesses. This graphical analysis further highlights the wider convergence domains. Overall, the developed derivative-free eighth-order scheme provides a powerful and efficient tool for solving nonlinear equations with multiple roots of known multiplicity, combining theoretical order of convergence with strong numerical performance in various applications.
11:30 AM – 11:50 AM 115-C Short Communications

Canonical Coordinates for Moduli Spaces of Connections on Curves and Geometric Painlevé Property of Isomonodromic Differential Equations

In this talk, we study a geometric counterpart of the cyclic vector which allow us to put a meromorphic connections on a curve into a “companion” normal form. This allow us to naturally identify an open set of the moduli space of connections (with fixed generic spectral data, i.e. unramified, non resonant) with some Hilbert scheme of points on the twisted cotangent bundle of the curve. We prove that this map is symplectic, therefore providing Darboux (or canonical) coordinates on the moduli space, i.e. separation of variables. We will also discuss about Riemann-Hilbert correspondences from moduli spaces of connections to moduli spaces of generalized monodromy data (monodromy data and Stokes data). We also review on a result of Inaba-Iwasaki-Saito about a proof of Painlevé property of all isomonodromic differential equations including Painlevé equations and Garnier equations. The Hamiltonian structure of these equaions can be understood by the canonical coordinates.
11:30 AM – 11:50 AM 119-AB Short Communications

Distal Actions of Automorphisms on the Space of One-Parameter Subgroups of Lie Groups

In this talk, I will discuss the action of automorphisms of a connected Lie group $G$ on Sub$_G$, the compact space of closed subgroups of $G$ endowed with the Chabauty topology. The compact space Sub$^p_G$, the closure in Sub$_G$ of the space of closed one-parameter subgroups of $G$, is invariant under this action. Automorphisms $T$ of $G$ which act distally on Sub$^p_G$ are characterized as follows:. If $G=\mathbb{R}^d$, a vector group, then $T$ acts distally on Sub$^p_G$ if and only if its image in PGL$(d,\mathbb{R})$ generates a relatively compact subgroup, and if $G$ is not a vector group, then $T$ acts distally on Sub$^p_G$ if and only if $T$ generates a relatively compact subgroup in Aut$(G)$. Distal actions of groups of automorphisms on Sub$^p_G$ are also characterized. Some of the results generalize those of Shah and Yadav in case $G$ is not a vector group. (This work is from two papers; one published jointly with Debamita Chatterjee, and the other written jointly with Himanshu Lekharu and Debamita Chatterjee.)
11:30 AM – 11:50 AM 118-C Short Communications

Finner-Like Inequalities in the Heisenberg Group

We completely characterize the range of $L^p$-boundedness of certain multilinear Radon-like transforms involving vertical projections in the Heisenberg group.
11:30 AM – 11:50 AM 120-AB Short Communications

Rigidity of Compact Quasi-Einstein Manifolds with Boundary

In this talk, we will discuss the classification of compact quasi-Einstein manifolds with boundary and constant scalar curvature. It is known by the classical book "Einstein Manifolds" (1984) that a quasi-Einstein manifold corresponds to a base of a warped product Einstein metric. Another interesting motivation to investigate quasi-Einstein manifolds derives from the study of diffusion operators by Bakry and Emery (1985), which is linked to the theories of smooth metric measure spaces, static spaces and Ricci solitons.We will show that a $3$-dimensional simply connected compact quasi-Einstein manifold with boundary and constant scalar curvature must be isometric to either the standard hemisphere $\Bbb{S}^3_{+},$ or the cylinder $I\times \Bbb{S}^2$ with product metric. For dimension $n=4,$ we prove that a $4$-dimensional simply connected compact quasi-Einstein manifold with boundary and constant scalar curvature is isometric to either the standard hemisphere $\Bbb{S}^4_{+},$ or the cylinder $I\times \Bbb{S}^3$ with product metric, or the product space $\Bbb{S}^2_{+}\times \Bbb{S}^2$ with the product metric. Other related results for arbitrary dimensions are also discussed. This is a joint work with Johnatan Costa and Detang Zhou.
11:30 AM – 12:30 PM Terrace Ballroom Plenary Lecture

Structure of Sets with an Unexpected Number of Arithmetic Patterns

We survey the interplay between ergodic theory and additive combinatorics over the past few decades, tracing the path from foundational ideas to higher-order Fourier analysis and onward to its modern applications and the open questions that continue to shape the field.

11:30 AM – 11:50 AM 115-A Short Communications

Upper Bound for the F-Threshold of Determinantal Rings

In this talk, we discuss a new upper bound for the $F$-threshold $c^{\mathcal{m}}(\mathcal{m})$ of determinantal rings generated by maximal minors by using a combinatorial approach. We prove that $c^\mathcal{m}(\mathcal{m})$ coincides with the negative $a$-invariant in the case of $3\times n$ and $4\times n$ matrices and we conjecture such equality holds for all matrices. This is a joint work with Barbara Betti, Alessio Moscariello and Francesco Romeo.
11:50 AM – 12:10 PM 119-AB Short Communications

A Comparative Study Investigating the Influence of Thermoelastic Coupling on Surface Wave Propagation in a Piezothermoelastic Half-Space

This investigation elucidates the propagation characteristics of surface (Rayleigh-type) waves within a homogeneous, transversely isotropic, piezothermoelastic half-space subjected to stress-free boundary conditions, with electrically open or shorted configurations, and thermally insulated or isothermal conditions. The analysis is grounded in the Green-Naghdi Type III (GN-III) and three-phase-lag thermoelastic models. Plane harmonic wave solutions are employed to determine mechanical displacements, electrical potential, and temperature variations. Utilizing these expressions, the corresponding stresses, electrical displacement, and temperature gradient are derived. Four secular equations are formulated for the considered half-space, contingent upon the specified boundary conditions. The trajectory of surface particles is shown to follow an elliptical path in the vertical plane aligned with the direction of wave propagation, with the eccentricity of the ellipse quantified. In cases where no phase difference exists between the vertical and horizontal displacement components, the particle trajectory degenerates into a straight line. A previously established analysis is presented as a specific case within this study. The influence of key wave characteristics, including phase velocity, attenuation coefficient, and specific energy loss, is graphically illustrated for the GN-III and three-phase-lag thermoelastic models, utilizing cadmium selenide material exhibiting hexagonal symmetry. The proposed mathematical framework holds potential for applications in the design and development of temperature sensors and other piezoelectric surface acoustic wave (SAW) devices.
11:50 AM – 12:10 PM 116-A Short Communications

Construction of a Family of Quantum Codes Using Sub-Exceding Functions via the Hypergraph Product and the Generalized Shor Construction

In this paper, we introduce a new family of stabilizer quantum codes constructed from the classical codes $L_k$ and $L_k^+$, which are defined via sub-exceding functions. By combining the hypergraph product method with the generalized Shor construction, we obtain quantum codes exhibiting a rich combinatorial structure and promising properties, particularly in terms of locality, low-density parity-check (LDPC) structure, and asymptotic parameters.Quantum error-correcting codes play a central role in protecting quantum information and ensuring the reliability of quantum computing systems. In previous work, we introduced the classical linear codes $L_k$ and $L_k^+$ based on sub-exceding functions and showed that they exhibit good performance in terms of minimum distance, decoding efficiency, and structural simplicity.More precisely, for any integer $k \geq 3$, the binary linear code $L_k$ has parameters $[2k, k]$, with a minimum distance equal to $3$ for $k = 3$ and $4$ for $k \geq 4$. The code $L_k^+$ has parameters $[3k, k]$, and its minimum distance is equal to $5$ for $k = 4$ and $6$ for $k \geq 5$. These properties indicate that both codes satisfy essential requirements such as fast information processing, reliability, and flexibility, making them suitable for quantum code constructions.The main objective of this work is to extend these classical constructions to the quantum setting by developing a new family of quantum codes based on $L_k$ and $L_k^+$. Using the hypergraph product technique together with the generalized Shor construction, we derive, for any positive integer $k$, a family of quantum LDPC codes with parameters$[[6k^2, k^2, d]]$,where the minimum distance $d$ is equal to $3$ for $k = 3$ and $4$ for $k \geq 4$.This construction provides a new combinatorial framework for the design of quantum LDPC codes and opens perspectives for further research on parameter optimization and decoding methods.
11:50 AM – 12:10 PM 115-B Short Communications

Dual Reciprocity Boundary Element Analysis of Magneto-Thermo-Bioconvective Flow in a Porous Square Cavity Saturated with Oxytactic Microorganisms

This study investigates magnetohydrodynamic (MHD) thermo-bioconvection of oxytactic microorganisms in a differentially heated, two-sided lid-driven porous cavity, considering the combined effects of thermal gradients, lid motion, magnetic fields, and porous media. The impact of key parameters on flow structure, temperature distribution, oxygen concentration, and microorganism density is analyzed in detail. The governing two-dimensional, steady, laminar, incompressible Newtonian flow equations are formulated under the Boussinesq approximation. The transport of oxytactic microorganisms is modeled using an augmented continuum framework. Numerical simulations are carried out using the Dual Reciprocity Boundary Element Method (DRBEM), which transforms domain integrals arising from source terms into equivalent boundary integrals through a dual reciprocity formulation. This method offers high computational efficiency and accuracy by reducing the dimensionality of the problem and requiring discretization only at the boundaries, making it especially suitable for complex coupled transport phenomena in porous media. Results show that the strength and orientation of the magnetic field, along with lid velocity and direction, significantly alter bioconvective flow patterns and species distribution. Higher concentrations of oxygen and microorganisms are observed near the upper cavity region. The findings highlight the sensitivity of bioconvective transport to multi-physical interactions and suggest potential applications in bio-engineering and industrial systems involving active suspensions.
11:50 AM – 12:10 PM 118-C Short Communications

Equivariant Structure of the Cohomologies of Curves

The study of the cohomology of algebraic varieties equipped with an action of a finite group is a classical and well-developed area. In this talk, I present new results on the Hodge, de Rham, and crystalline cohomology of smooth projective curves endowed with an action of a finite $p$-group in characteristic $p$.I show that the Hodge and de Rham cohomologies of an arbitrary $p$-group cover admit a decomposition into a global part and local parts. The global part depends only on the 'topology' of the cover (i.e. the stabilizer groups and the quotient curve). The local parts arise from Harbater–Katz–Gabber covers that approximate the cover over a given point. This extends my earlier results for generic covers and generalizes a theorem of Nakajima in the étale case.I then address the analogous question for crystalline cohomology. Although such a decomposition is not known in general, I present a new result for $\mathbb Z/p^n \mathbb Z$-covers which provides evidence that a similar local–global phenomenon should hold in this setting as well.
11:50 AM – 12:10 PM 118-AB Short Communications

Modeling and Numerical Approximation of Bilayer Water and Gas Flows in Pipelines

We present a new model for bilayer water flows along pipelines. The bottom layer consists of an incompressible liquid state, governed by the shallow-water equations. The top layer is a compressible gaseous fluid, which exchanges momentum with the lower layer. During the talk, we will present the derivation of the model along with a description of its hyperbolic properties. We also propose a high-resolution, non-oscillatory, semi-discrete central scheme to approximate solutions. This scheme extends existing semi-discrete central methods for hyperbolic conservation laws. The system is integrated in time using a second-order Runge-Kutta scheme with strong stability preservation. Along with a detailed description of the scheme and a demonstration of these two properties, we present several numerical experiments that show the robustness of the algorithm. This is a joint work with Gerardo Hernández Dueñas.
11:50 AM – 12:10 PM 120-AB Short Communications

Primitive Invariants from Laminations

Combining geometric group theory techniques with geometric topology tools, we show how primitive cohomologies provide useful insights towards unifying the mathematical formulation of Gromov-Witten invariants. In particular, we emphasise the role played by geodesic laminations in analysing such invariants for the case of complete intersections in projective space.
11:50 AM – 12:10 PM 115-A Short Communications

Semigroup Actions on 2x2 Tropical Matrices

Tropical algebra is a semiring where the addition and multiplication operations are replaced by maximum and addition, respectively. Within this algebraic structure, tropical matrices form semigroups under tropical matrix multiplication. Among the most fundamental algebraic ideas connected to semigroups is that of a semigroup action.%The concepts of semigroup actions have been discussed on posets and preimage quasi-orders and on sets and the burnside ring. But, it has not been discussed in the context of a tropical setting.This paper discusses the concept of semigroup actions defined by $2\times2$ tropical matrices, examining their properties such as freeness, transitivity, and regularity.
11:50 AM – 12:10 PM 115-C Short Communications

Uniform Rationality and Related Properties

In 1989, motivated by applications to Oka theory, M. Gromov asked whether every smooth rational complex algebraic variety $X$ is uniformly rational, meaning that each point of $X$ admits a Zariski open neighbourhood isomorphic to a Zariski open subset of the affine space. Despite a promising attempt at solving it in the affirmative using the Weak Factorization Theorem, it still remains open. In my talk, I will describe two alternative versions of this problem, where instead of rationality one considers different birationally invariant properties (stable rationality and retract rationality), and discuss my recent solutions to these versions.
12:10 PM – 12:30 PM 115-B Short Communications

Factorization Problems of $p$-adic $L$-functions Arising in Iwasawa Theory

The goal is to explain factorization phenomena for certain $p$-adic $L$-functions, guided by the Artin formalism. I will begin by recalling some background and previously known results in the setting of $\mathrm{GL}_2$ and $\mathrm{GL}_2 \times \mathrm{GL}_2$. I will then describe some of our recent work on factorization problems for triple products of Hida families and for twisted triple products of Hilbert modular forms over real quadratic fields. The proofs are largely based on comparisons between different Euler systems arising in these settings. Finally, I will give sketches of the proofs in selected cases, illustrating both analytic and algebraic factorization results, with an emphasis on the main ideas rather than technical details. These are joint works with K. B\"uy\"ukboduk, D. Casazza, CdV Piquero and B. Das.
12:10 PM – 12:30 PM 120-AB Short Communications

Homological Ideals Over Auslander Algebras of Radical Square Zero Algebras of Dynkin Quiver

The notion of homological ideals was introduced by M. Auslander et al. in 1992; they referred to them as strong idempotent ideals. These ideals exhibit several interesting properties and have been further studied by Gatica, Lanzilotta, and Platzeck to explore their connections with the Finitistic Dimension Conjecture. In this talk, we will describe some of the main properties of these ideals, and we will generalize ideas given in 2023 by A. Moreno Cañadas and P. F. Fernández Espinosa to provide a combinatorial description of the number of homological ideals in Auslander algebras of radical-square-zero Dynkin algebras.
12:10 PM – 12:30 PM 119-AB Short Communications

Integrable Multi-Species Long-Range Swap Models

We introduce and study new integrable long-range swap models for multi-species interacting particle systems on the one-dimensional lattice. Particles are labeled by natural numbers, interpreted as species, with larger labels corresponding to stronger particles. Empty sites are treated as particles of species 0.Each particle waits an independent exponential time of rate 1, and upon activation searches to the right for the nearest weaker particle. When such a weaker particle is found, the two particles exchange their positions, producing a long-range swap. The resulting dynamics define non-local interacting particle systems that extend classical exclusion-type processes.A key feature of the model concerns how a particle treats sites occupied by particles of the same species during the search for a weaker particle. We construct two distinct integrable versions of the long-range swap dynamics. In the pushing version, a jumping particle treats particles of the same species as stronger, which leads to pushing-type dynamics among same-species particles and generalizes the single-species drop-push model. In the blocking version, particles of the same species are treated as weaker, so that no movement occurs when the nearest weaker particle to the right has the same label, thereby generalizing the usual single-species TASEP when interpreted as a short-range swap model.Despite their different microscopic behaviors, both dynamics admit a unified algebraic description. Integrability is established through the analysis of two-particle interaction matrices satisfying Yang-Baxter-type relations, ensuring the consistency of the many-particle dynamics. Moreover, this construction yields a new continuous family of integrable long-range swap models, obtained via convex interpolation between the pushing and blocking dynamics.We also provide explicit formulas for the transition probabilities of finite N-particle systems for arbitrary initial configurations.
12:10 PM – 12:30 PM 118-C Short Communications

Long Paths Need Not Minimize $H$-Colorings Among Trees

Given a graph $G$ and a target graph $H$, an $H$-coloring of $G$ is an adjacency-preserving vertex map from $G$ to $H$. By appropriate choice of $H$, these colorings can express, for instance, the independent sets or proper vertex colorings of $G$. Sidorenko proved that for any $H$, the $n$-vertex star admits at least as many $H$-colorings as any other $n$-vertex tree, but the minimization question remains open in general. For many graphs $H$, path graphs are among the trees with the fewest $H$-colorings, but work of Leontovich and subsequently Csikvari and Lin shows that there is a graph $E_7$ on seven vertices and a target graph $H$ for which there are strictly fewer $H$-colorings of $E_7$ than of the path on seven vertices.We introduce a new strategy for enumerating homomorphisms from path-like trees to highly symmetric target graphs that allows us to make the previous observations completely explicit and extend them to infinitely many $n$ beyond $n=7$. In particular, we exhibit a target graph $H$ with the property that for each sufficiently large $n$, there is a tree $E_n$ on $n$ vertices that admits strictly fewer $H$-colorings than the path on $n$ vertices.
12:10 PM – 12:30 PM 116-A Short Communications

On a Method for Solving the Riccati Equation

\begin{document}\maketitleThe Riccati differential equation, encountered in various fields of science and engineering since 1724, has attracted the attention of mathematicians and engineers. With the advent of optimal control theory in the 20th century, interest in the Riccati equation significantly increased. When solving the problem of synthesizing optimal control, the Riccati equation appears in either differential or algebraic form. However, finding an explicit solution to the Riccati equation is possible only in special cases. This is because, despite extensive research spanning over 300 years, no algorithm has yet been developed for constructing particular solutions of the Riccati equation!This paper presents the results of investigations into additional properties of the Riccati equation. It has been established that there exist certain Riccati equations whose particular solutions can be determined using known analytical methods, for example, via particular solutions of linear non-homogeneous differential equations. Such Riccati equations possess specific properties, and we refer to the set of such equations as the class of coefficient-conjugate Riccati equations. Furthermore, it has been proven that if a particular solution of a coefficient-conjugate equation is known, then it is possible to find a particular solution of a Riccati equation with arbitrarily given coefficients.It should be noted that if a particular solution of the Riccati equation is known, then, based on the well-known properties of the Riccati equation, one can also find particular solutions of second-order linear differential equations and second-order linear systems with variable coefficients.It has been shown that the developed algorithm for constructing particular solutions of coefficient-conjugate scalar equations can be generalized to matrix differential Riccati equations.Similar results have been obtained for both scalar and matrix algebraic Riccati equations.In conclusion, an example of solving an optimal control synthesis problem is presented, where the solution of the Riccati equation can be determined without significant difficulties.\end{document}
12:10 PM – 12:30 PM 118-AB Short Communications

On the Global Regularity of the Navier-Stokes Equations

We establish a sufficient condition on the initial data that ensures the existence of global smooth solutions to the incompressible Navier-Stokes equations on $\mathbb{R}^d$, for dimensions $d\geq 3$. The solutions constructed exhibit rapid decay at spatial infinity, satisfying the physical energy bounds expected of physically reasonable flows. Furthermore, we demonstrate that, for positive times, the velocity and pressure fields admit an analytic extension to the complex domain, forming a smooth curve of entire vector fields of order two. Our results provide new insights into the structure and regularity of Navier-Stokes flows under explicit and verifiable conditions on the initial data.
12:10 PM – 12:30 PM 115-C Short Communications

On the Use of the Concentration Function to Compare Predictive Distributions in ARMA Models

In this study, we propose the use of the concentration function as a novel tool for assessing the adequacy of predictive distributions in a Bayesian framework. The methodology relies on a rolling-origin evaluation strategy, in which the available time series is partitioned into two segments: the first is used for model estimation, while the second is used for out-of-sample prediction. The concentration function is then constructed for each set of forecasts, providing a distributional assessment of predictive performance across competing models. In this framework, the model with the least inequality in its concentration function is interpreted as offering superior predictive fit. To complement this curve-based analysis, we compute two well-established inequality measures—the Gini concentration coefficient and the Pietra index— which provide further evidence and consistency regarding model performance. These measures allow for a comprehensive evaluation of how closely predictive distributions align with observed outcomes. The proposed methodology is validated through a simulation study, in which its ability to discriminate between models is assessed under controlled conditions. We illustrate its practical applicability by analyzing real-world data, thus demonstrating the usefulness of concentration functions and associated inequality measures as diagnostic tools for Bayesian predictive evaluation.
12:10 PM – 12:30 PM 115-A Short Communications

Simple Derivations and Isotropy Groups

In the talk, we will discuss the simple derivations and the structure of isotropy groups according to a simple derivation.
12:30 PM – 12:50 PM 118-C Short Communications

Between l and l+2: Cycles in 2-player Strong Ramsey Games

\noindent Let the strong Ramsey game $R(K_n,H)$ be where two players $P_1$ and $P_2$, each acting as both attacker and defender, are alternately claiming previously unclaimed edges of a complete graph $K_n$ on vertex set $[n]=\{1,2,3,....,n\}$ . The first player to claim a set of edges that contains a subgraph, isomorphic to a given target graph $H$, is said to win (otherwise the game may end in a draw). Bounded-time, strong Ramsey games are defined to be (DHT 2017 \cite{dht}; AGXY 2025 \cite{agxy}) the game defined by the parameter \[ L(K_n,H):=\min\{T:\text{Player 1 can force a win by their $T$-th move}\}.\]\noindent This work is focused on the cycled target graphs given by $H=C_\ell$. AGXY 2025 \cite{agxy} showed that for each fixed $\ell\ge 3$ and all sufficiently large $n$, \[ L(K_n,C_\ell)\le \ell+2,\] by first constructing a long path of length $\ell-2$ whose endpoints cannot be mirrored by the opponent. It is natural to ask next: beyond the (trivial) lower bound $L(K_n,C_\ell)\ge \ell$, can a strategy be devised by player $P_2$ to further delay $P_1$'s win, and if so, by how many moves? Our results provide an (additional-move) improvement in the case of triangles as the target graph, \textit{i.e.}, for all $n\ge 4$, \[\begin{equation} L(K_n,C_3)\ge 4 , \end{equation}\]using the local-threat elimination strategy, whereby $P_2$ ensures to not let $P_1$ achieve the $C_3$ configuration in its third move. Depth-limited minimax is used for $(H,T)=(C_4,5)$ to show that $P_1$ cannot force $C_4$ by their $5$th move for $n\ge 18$, whereas $P_1$ can force a $C_4$ by their $6$th move for all $n\ge 22$. Therefore, \[\begin{equation} L(K_n,C_4)=6 \qquad (n\ge 22)\end{equation}\] \noindent Similarly, for $(H,T)=(C_5,6)$ and $(C_5,7)$, $P_1$ cannot force $C_5$ by their $6$th move for any $n\ge 22$, but can force $C_5$ by their $7$th move for all $n\ge 26$, thus, \[L(K_n,C_5)=7 \qquad (n\ge 26),\]Taken together with the explicit upper bound $L(K_n,C_\ell)\le \ell+2$ for fixed $\ell$ and all sufficiently large $n$, these findings motivate the refined conjecture that, among cycles with $\ell \geq 4$, $L(K_n,C_\ell)=\ell+2$ and all sufficiently large $n$. It also answers our question as to whether $P_2$ can delay $P_1$'s win: for $\ell=5$ with sufficiently large $n$, $L(K_n,C_\ell) \neq \ell+1$ , suggests that $P_2$ can delay $P_1$'s win by two moves more than the trivial lower bound.
12:30 PM – 12:50 PM 118-AB Short Communications

Bifurcation Methods for a Class of Periodic Superlinear Boundary Value Problems

In this talk, I will apply bifurcation methods to an elliptic superlinear problem in one-dimension with periodic boundary conditions.One of the main novelties of this approach is that it allows the treatment of the case of bifurcation points in which the linearized operator has a two-dimensional kernel, leading to new local and global multiplicity results.I will consider specific examples where these methods apply, complementing the analytical results with numerical simulations.This work is in collaboration with Eudardo Muñoz-Hernández (Universidad Complutense de Madrid, Madrid, Spain) and Juan Carlos Sampedro (Universidad Politécnica de Madrid, Madrid, Spain).
12:30 PM – 12:50 PM 115-B Short Communications

For This Ramsey–Collatz Equivalence Relation on Bitspace(363), Computational Search Establishes Over 16,000 Classes (by Definition, Not Exceeding 20,017)

Our computational study concerns positive integers $n < 2^{363}$ (Bitspace(363)) under the Collatz map and a Ramsey weight function, focusing on the size of a resulting equivalence relation.The Collatz map is defined as $n \mapsto n/2$ if even, and $n \mapsto (3n+1)/2$ if odd. Define the stopping time $c(n)$ as the number of steps to reach $1$, or infinity if no such step exists. Stopping times are here partitioned into four categories: $c < 700$, individual values $700$--$3199$, $c \ge 3200$, and infinity.The Ramsey weight $w(n)$ is derived from binary digits of $n$ labeling edges of a ternary tree of depth $5$ (padding with leading zeros as needed); the smallest root-to-leaf path count across all binary subtrees gives $w(n) \in \{1,\dots,8\}$.Considering equivalence classes by paired $(c,w)$-values (with merging for extreme $c$-ranges and merging $w$-values if $c$ is infinity), the absolute upper bound is $20{,}017$ classes.Our computational search establishes a lower bound of $16{,}022$ classes ($16{,}874$ without merging), including $1{,}595$ weight-8 classes and nine of the potentially 16 merged classes for $c < 700$ or $c \ge 3200$. We also achieve long consecutive stopping-time ranges for weights $1$--$8$ (e.g., weight $1$ spans $[1,2585]$). These results reveal significant structural diversity within Bitspace(363) under Collatz dynamics combined with Ramsey-theoretic constraints.
12:30 PM – 12:50 PM 120-AB Short Communications

Functional Identities Involving Inverses Over Division Rings

In the context of ring theory, a functional identity (FI) is defined as an equation that holds for all elements in a ring and involves unknown maps acting upon those elements. As a specialized and rigorous branch of algebra, the Theory of Functional Identities systematically investigates the precise forms of such maps and explores how their existence dictates the underlying structural properties of the algebra, such as its commutativity or dimensionality.This work investigates the evolution of FIs, starting from the classical roots of Cauchy’s additive functions in 1821 to Israel Halperin’s provocative 1963 challenge in the "New Scottish Book," which catalyzed the study of modern rational functional identities. Our focus lies at the intersection of these historical problems and cutting-edge algebraic techniques, specifically within the framework of non-commutative division rings.We present a complete and unified characterization of the general identity $f(x) = x^n g(x^{-1})$ for all invertible elements $x$, where $f$ and $g$ are additive maps on a division ring $D$. While existing literature has predominantly addressed specific cases for $n=1, 2, 3,$ and $4$, this presentation unveils recent findings that provide a definitive and comprehensive solution for all integers $n \geq 0$. A key highlight of our results is the striking structural transition occurring at $n=2$: we demonstrate that while the identity forces a specific structural form when $n=2$, it collapses into the standard zero solution for all other cases. This is joint work with T.-K. Lee and J.-H. Lin.\vspace{0.5cm}\noindent \textbf{Keywords:} Functional Identities, Division Rings, Additive Maps, Characteristic 2, Hua's Identity.
12:30 PM – 1:30 PM Breaks

Lunch on Own

12:30 PM – 12:50 PM 119-AB Short Communications

Probabilistic Nontrivial Solutions to the Equation X^n = Y^n + Z^n

\documentclass[12pt]{article}\usepackage{latexsym,amsmath,amssymb} \textheight 650pt\textwidth 420pt \oddsidemargin 20pt \begin{document}\noindent Probabilistic Nontrivial Solutions to the Equation $X^n = Y^n + Z^n$\vspace{0.3cm}\noindentJordan M. Stoyanov \\Bulgarian Academy of Sciences, Sofia, Bulgaria \vspace{0.3cm}\noindent For an arbitrary random variable $X$ with finite all moments and a natural $n$, we construct random variables $Y$ and $Z$ such that $X = Y + Z$ and derive a 'Fermat-type' equation, $X^n = Y^n + Z^n.$ Notably, we prove that both $Y^n$ and $Z^n$ satisfy the classical Carleman's condition, ensuring that they are moment-determinate. Importantly, these decompositions hold true universally, regardless of whether $X$ and $X^n$ are moment-determinate. It is unusual to see a moment-indeterminate random variable expressed as a sum of two moment-determinate variables. As a consequence we derive another nontrivial statement telling that a non-analytic characteristic function can be represented as a convex mixture of quasi-analytic functions.These decompositions constitute the key results intended for presentation at the ICM – 2026. Our results encompass both the Hamburger case, where $X$ is on the entire real line, and the Stieltjes case, where $X$ is confined to the positive half-line. While it is easier to work with moment-determinate $X$ or $X^n$, our research provide new results revealing unusual properties of moment-indeterminate variables. The results are illustrated by examples involving moment-indeterminate powers of random variables that follow normal, exponential, or logistic distributions. Our results are novel, nontrivial, and essential for understanding deep properties of random variables in terms of their moments and associated characteristic functions. This work is joint with Gwo Dong Lin (Academia Sinica, Taipei, Taiwan, RoC).\end{document}
12:30 PM – 12:50 PM 115-A Short Communications

Stochastic Predictability and Applications in Credit Risk Theory

In this talk, we will explore the concept of stochastic predictability introduced in [A. Merkle, Causal predictability and weak solutions of the stochastic differential equations with driving semimartingales, Statistics and Probability Letters, 197(C) (2023)]. This notion is grounded in the stochastic definition of causality within continuous-time models and captures a form of dependence between stochastic processes and filtrations. We will also examine some of the properties that have been developed since its introduction. Examples will be provided to illustrate the application of the concept of stochastic predictability to local martingales, along with its connections to well-established ideas in probability theory, stochastic differential equations, and related fields. In addition, we will apply this framework to diffusion-type processes, with particular emphasis on the uniqueness of weak solutions to Ito stochastic differential equations and those driven by semimartingales. The talk will conclude with a focus on applications in financial mathematics, especially in the modeling of credit risk.
12:30 PM – 12:50 PM 115-C Short Communications

The Geometry of Three Pairwise Comparisons: Extension to Discrete Random Variables with Ties

In many applied disciplines, including engineering and economics, inference is frequently based on pairwise comparisons rather than univariate summaries. These head-to-head comparisons - unlike univariate statistics - may be non-transitive. The violation of transitivity has been observed across diverse fields. In sports, the cyclic dominance pattern where player A tends to defeat B, B tends to defeat C, and C tends to defeat A, is often treated as a paradoxical curiosity. In economics, non-transitivity constitutes a fundamental violation of rational preference, addressed by the Arrow and Debreu Theorems. In evolutionary biology, analogous cyclic interactions have been proposed as a mechanism sustaining species diversity, a hypothesis supported by experimental evidence.The mathematical structure underlying such phenomena was discussed in the 1930s and 1940s by mathematicians of the Scottish Café school, including Steinhaus. Later, his student, Stanisław Trybuła, provided a complete characterization of the comparison space for three random variables. In this work, we report two contributions. First, intuitively, one might expect the Trybula space to be symmetric with respect to the three coordinates. We confirmed this geometric intuition by providing a reformulation of Trybula's Theorem that exhibits explicit symmetry. Second, we extended Trybula's result to discrete random variables with ties. Our prior work has shown how the Trybula result can be used in the context of clinical trials to rule out non-transitivity between treatments. However, in the case of clinical trials, one of the assumptions of Trybula, that the probability of ties is zero, can be frequently violated if we work with discrete time. E.g., deaths are reported per day, per week, or per month. Our work resolves this issue by extending the Trybula result for discrete random variables with ties.
12:30 PM – 12:50 PM 116-A Short Communications

Tracking Problem in Nonlinear Optimization of Oscillation Processes

In optimal control theory, there exists a class of problems in which the control objective is to minimize the deviation of a controlled process from a prescribed trajectory over the entire control horizon. Such problems are referred to as tracking problems.This paper investigates the solvability of a tracking problem within the framework of nonlinear vector optimization of oscillatory processes described by integro-differential equations in partial derivatives with a Fredholm integral operator, under the assumption that the scalar functions of external and boundary actions depend nonlinearly on the components of the vector controls.The analysis is carried out using the maximum principle for distributed parameter systems. The resulting optimality condition leads to a system of equality relations with respect to the components of both the distributed vector control and the boundary vector control. Therefore, the components of the optimal distributed and boundary controls are determined as solutions of a system of two nonlinear integral equations.A methodology for studying the unique solvability of this nonstandard system is developed. In particular, by introducing new functions defined on a closed domain, the system of two nonlinear integral equations is reduced to an equivalent scalar nonlinear integral equation. The unique solvability of the resulting scalar equation is investigated using the contraction mapping principle, and sufficient conditions for the existence of a solution are established.Based on these results, the optimal distributed and boundary vector controls are constructed, the optimal process is determined, and the minimum value of the cost functional is computed. Thus, for the case of distributed and boundary vector controls, a methodology for constructing a complete solution to the tracking problem in nonlinear optimization of oscillatory processes described by integro-differential equations in partial derivatives with a Fredholm integral operator is proposed.
12:50 PM – 1:10 PM 116-A Short Communications

A Three-Stage Green Multi-Objective Multi-Item Fixed-Charge 5-dimensional Transportation Problem Under an Intuitionistic Fuzzy Environment

Sustainable transportation has emerged as a key global concern, driving the need for optimization models that promote environmentally responsible logistics planning and management. This study introduces a three-stage green multi-objective, multi-item fixed-charge five-dimensional transportation problem (GMMFC-5DTP) that explicitly incorporates sustainability considerations into transportation decision-making. A notable contribution of this work is the novel inclusion of driver behavior in carbon emission estimation, demonstrating that driver-specific characteristics have a substantial impact on emission levels. To realistically capture uncertainty in transportation parameters, trapezoidal intuitionistic fuzzy numbers are employed. Due to the model’s high dimensionality and uncertain environment, advanced evolutionary optimization techniques are required. Accordingly, the non-dominated sorting genetic algorithms NSGA-II and NSGA-III are applied. In support of these algorithms, a feasible initial population generation strategy and a feasibility-preserving mutation operator are proposed, representing important methodological contributions. The effectiveness of the framework is validated through a numerical illustration. The results indicate that NSGA-III significantly outperforms NSGA-II, generating a much richer and more evenly distributed set of Pareto-optimal solutions for the three-stage GMMFC-5DTP. The findings further emphasize the critical influence of vehicle type, routing choices, and driver behavior on carbon emissions, offering practical insights for sustainable transportation planning. Overall, the proposed approach delivers clear and effective guidance for achieving greener and more efficient transportation decisions under uncertainty.
12:50 PM – 1:10 PM 118-AB Short Communications

Fujita Critical Exponents for the Semilinear Parabolic Problems

This work explores the critical behavior of the semilinear heat equation $$u_t+\mathcal{L}_{a, b}u=|u|^p+f(x),\,t>0,\,x\in\mathbb{R}^d,\,d\geq 2,$$ considering both the presence and absence of a forcing term $f(x).$ The mixed local-nonlocal operator $$\mathcal{L}_{a, b}=-a\Delta+b(-\Delta)^s,\,a,\,b \in \mathbb{R}_+,\,s\in(0,1),$$ incorporates both local and nonlocal Laplacians. We determine the Fujita-type critical exponents:$$p_{Crit}=\left\{\[\begin{array}{cc} 1+\frac{2s}{d}, & \text{if},\,\,f\equiv 0, \\{}\\ 1+\frac{2s}{d-2s}, & \text{if},\,\,f\not\equiv 0,\end{array}\]\right.$$by considering the existence or nonexistence of global solutions. Interestingly, the critical exponent is determined by the nonlocal component of the operator and, as a result, coincides with that of the fractional Laplacian. In the case without a forcing term, our results improve upon recent findings by Biagi et al. [Bull. London Math. Soc. (2024), 1–20] and Del Pezzo et al. [Nonlinear Analysis, 255 (2025), 113761]. When a forcing term is included, our results refine those of Wang et al. [J. Math. Anal. Appl., 488 (1) (2020), 124067] and complement the work of Majdoub [La Matematica, 2 (2023), 340–361].
12:50 PM – 1:10 PM 115-A Short Communications

Mathematical Modeling of the Synergistic Anti-Cancer Effects of Combined Vesicular Stomatitis and Vaccinia Viruses

This research investigates the synergistic effects of combining Vaccinia (VV) and Vesicular stomatitis (VSV) oncolytic viruses for cancer treatment. A mathematical model, based on an experiment where the combination of VV and VSV demonstrated synergistic oncolytic activity in vitro and in vivo, is constructed and analysed. The model is subsequently fitted to the experimental data and parameters are estimated. The model’s transient and qualitative behavior is characterized, generating new biological hypotheses to inform experimental validation and improve strategies for more effective tumor reduction. Global sensitivity analysis has been conducted to determine the parameters that most significantly influence the treatment outcome and several numerical simulations have been carried out to investigate the effect of different factors. Optimal time delays, representing the initial delivery timing of VV and VSV, which minimize tumor cell count during virus administration, have been determined.This is joint work with Raluca Eftimie, Anotida Madzvamuse, Rachid Ouifki, Amina Eladdadi and Helen Byrne.
12:50 PM – 1:10 PM 115-C Short Communications

Multivariate Dependencies in Multiplex Graphons

Pairwise interlayer dependence measures are insufficient to characterize multivariate dependence in random multiplex graphs. A simple example is the XOR construction: generate two layers independently and define a third as their edgewise XOR. The first two layers are marginally independent but dependent conditional on the third, so the dependence is intrinsically multivariate and missed by pairwise summaries. This motivates invariants of the full joint distribution that capture higher-order dependence. We construct such invariants and develop an estimation theory for them within the well-studied class of exchangeable multiplex graphs.By exchangeability, an $\ell$-layer multiplex ($\ell\ge2$ fixed) admits a multiplex graphon $\mathbf W_\ell=\{W_\gamma\}_{\gamma\in\{0,1\}^\ell}$ with $W_\gamma(x,y)\ge0$ and $\sum_{\gamma} W_\gamma(x,y)=1$ for $(x,y)\in[0,1]^2$, encoding the local law of the $\{0,1\}^\ell$-valued edge-state vector under a shared latent parametrization.Our contributions are twofold. First, we introduce the joint graphon entropy\[H(\mathbf W_\ell):=-\iint_{[0,1]^2}\sum_{\gamma\in\{0,1\}^\ell} W_\gamma(x,y)\log_2 W_\gamma(x,y)\,\mathrm{d}x\,\mathrm{d}y,\]show invariance under measure-preserving relabelings (so $H(\mathbf W_\ell)$ is well-defined on multiplex graph limits), and use it to define graphon-level multivariate information measures. In particular, we introduce a nonnegative graphon total correlation (and a conditional variant) that vanishes exactly when the $\ell$ layers are independent in latent space, and a signed graphon interaction information that separates redundancy from synergy and detects XOR-type dependence.Second, we construct a nonparametric estimator $\widehat{H}(\mathbf W_\ell)$ of $H(\mathbf W_\ell)$ and the derived invariants from a single observed $n$-vertex multiplex with $\ell$ layers. For multiplex graphons $\mathbf W_\ell$ with Hölder$(\alpha)$ components ($\alpha\in(0,1]$),\[\big|\widehat H(\mathbf W_\ell)-H(\mathbf W_\ell)\big|= O_{\mathbb P}\!\big(R_n\log(1/R_n)\big),\qquadR_n^2 = n^{-\frac{2\alpha}{\alpha+1}}+\frac{\log n}{n}+n^{-\alpha},\]with the same rate for graphon total correlation and graphon interaction information; here $R_n^2$ is the standard Hölder$(\alpha)$ $L^2$ graphon rate (also for multiplex graphons with fixed $\ell$). Together, this yields graphon-invariant multivariate dependence functionals estimable from one multiplex graph.

Joint with Sofia Olhede (EPFL)

12:50 PM – 1:10 PM 120-AB Short Communications

On Structural Aspects of Essential Ideals in Matrix Nearrings and Group Nearrings

On structural aspects of essential ideals in matrix nearrings and group nearringsSyam Prasad Kuncham#1, Rajani Salvankar2, Tapatee Sahoo3, Babushri Srinivas Kedukodi4 and Harikrishnan Panackal5 1,2,4,5Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal – 576 104, India. 3Department of Mathematics, Manipal Institute of Technology Bengaluru Campus.Manipal Academy of Higher Education, Bengaluru-560064, India #Presenting Author: Email: syamprasad.k@manipal.eduAbstract Essential submodules play a vital role in the study of finite Goldie dimension in modules over associative rings. In this work, we extend these ideas to modules over nearrings. Nearrings are natural generalizations of associative rings in which addition need not be commutative and only one distributive law holds. We introduce the concept of essential ideals in matrix nearrings and establish several properties that highlight the interplay between nearrings and their corresponding matrix nearrings. Furthermore, we the study of essential ideals to group nearrings and explore their structural aspects. Finally, we prove the properties of graphs associated with these ideals and illustrate the results through suitable examples.AMS Classification: 16Y30Keywords: Matrix Nearring, Module over a Nearring, Essential ideal, Complement ideal # Presenting Author
12:50 PM – 1:10 PM 115-B Short Communications

On a Non-Archimedean Analogue of a Question of Atkin and Serre

In this talk, we will discuss a non-Archimedean analogue of a question of Atkin and Serre. More precisely, we will discuss lower bounds for the largest prime factor of non-zero Fourier coefficients of non-CM normalized cuspidal Hecke eigenforms of even weight $k \geq 2$, level $N$ with integer Fourier coefficients. In particular, we will show that for such a form $f$ and for any real number $\epsilon>0$, the largest prime factor of the $p$-th Fourier coefficient $a_f(p)$ of $f$, denoted by $P(a_f(p))$, satisfies$$P(a_f(p)) ~>~ (\log p)^{1/8}(\log\log p)^{3/8 -\epsilon}$$for almost all primes $p$. This improves a result of Ram Murty, Kumar Murty, Saradha. Further, assuming the generalized Riemann hypothesis (GRH), we will show that there exists a positive constant $c$ such that the set of primes $p$ for which$$P(a_f(p)) ~>~ c p^{1/14} (\log p)^{2/7}$$has lower density at least $1-\frac{2}{13(k-1)}$. Further, we extend these results to Fourier coefficients at natural numbers $n$ using Brun's sieve. More precisely, we will show that the set$$\left\{n \in \mathbb{N} ~:~ a_f(n) = 0 \text{ or } P(a_f(n)) > (\log n)^{1/8} (\log\log n)^{3/8 -\epsilon} \right\}$$has natural density equal to $1$. We also discuss a number field analogue of a recent result of Bennett, Gherga, Patel and Siksek about the largest prime factor of $a_f(p^m)$ for $m \geq 2$. This is a joint work with Yuri F. Bilu and Sanoli Gun.
12:50 PM – 1:10 PM 118-C Short Communications

Spectral w-variation of Graphs in Two Places

This work is based on the article [Parameswar Basumatary, Debajit Kalita, Spectral w-variation of trees in two places, Linear Algebra and Its Applications, 718, (2025) 81-103]. A weighted graph $G$ is said to have spectral $w$-variation in two places if adding an edge of positive weight $w$ between two nonadjacent vertices of $G$, or increasing the weight of an existing edge by $w$, results in an increase of two Laplacian eigenvalues of $G$ equally by $w$ while keeping the other eigenvalues unchanged. We characterize the weighted graphs that have spectral $w$-variation in two places. It is proved that spectral $w$-variation in two places does not occur by increasing the weight of an existing edge in any weighted tree. Primarily, we determine the weighted trees that have spectral $w$-variation in two places. As an application, we supply constructions of few classes of weighted trees with weights from the interval $(0,1)$ in which spectral $w$-variation occurs in two places.
12:50 PM – 1:10 PM 119-AB Short Communications

The Smallest Singular Value of Large Random Rectangular Toeplitz and Circulant Matrices

Joint work with Alexei Onatski (University of Cambridge). We consider rectangular Toeplitz and rectangular circulant random matrices built from an i.i.d. standard Gaussian sequence. When the dimensions grow proportionally (rows/columns converges to a constant in (0,1]), we prove that the smallest eigenvalue of the normalized sample covariance converges to zero in probability and in expectation. We further bound the convergence rate, showing it is faster than any polylogarithmic rate but slower than any polynomial rate. For the circulant model we obtain an explicit upper bound depending only on the aspect ratio, implying that for sufficiently small aspect ratios the decay can be arbitrarily slow on a polynomial scale.
1:10 PM – 1:30 PM 115-C Short Communications

A Unified Approach for Independence Testing in Mixed-Type Data

We consider the problem of testing independence in mixed-type data that combine count variables with absolutely continuous variables. After introducing test statistics in the bivariate setting for assessing independence between the components of a bivariate mixed-type vector, we extend them to the multivariate context to accommodate both testing independence between vectors of different types and possibly different dimensions, and testing total independence among all components of vectors with different types. The construction relies on a novel transformation that combines the probability generating function and the characteristic function to fully characterize the joint distribution of such data. We establish the asymptotic properties of the resulting tests and, through an extensive power study, demonstrate that the proposed approach is both competitive and flexible. Potential applications in variable selection problems are also discussed.
1:10 PM – 1:30 PM 116-A Short Communications

Backstepping Control and Stabilization of Stochastic Nonlinear Discrete-Time Systems with Time Delays

The stabilization for nonlinear discrete-time strict-feedback systems with Poisson noise and time delays is investigated. A backstepping control framework is proposed to design a stabilizing controller for the considered stochastic system which helps to overcome the causality contradiction that appears in the controller design. Under Lipschitz continuity assumptions on the nonlinearities, sufficient condition for exponential mean-square stability of the closed-loop system is derived using Lyapunov-Krasovskii theory. The results are novel and has some new contributions to the discrete-time strict-feedback stochastic systems with delays. Finally, numerical examples are presented to illustrate the effectiveness of the proposed control strategy.
1:10 PM – 1:30 PM 115-A Short Communications

Comparing Classical and Path Coupling Bounds in Finite-State Markov Chains: A Graph-Coloring Case Study

Bounding the convergence rate of Markov-chain Monte-Carlo (MCMC)samplers is central to probabilistic computation. Two populartechniques are (i) classical coupling, which constructs a jointprocess that coalesces, and (ii) path coupling, which verifies aone-step contraction in a chosen metric and lifts it to the wholestate space. Quantitative head-to-head comparisons on the "same"chain are rare. This work studies single-site Glauber dynamics for$q$-colourings of the four-vertex cycle~$C_{4}$ ($q\ge3$). We provide\[ \mathbf{E}[\tau_{\mathrm{cl}}]\le 6(q-1),\qquad \mathbf{E}[\tau_{\mathrm{pc}}]\le 2(q-1),\]where the latter follows from a Hamming path-coupling contraction$\alpha(q)=1-\tfrac{1}{2(q-1)}$. Consequently$t_{\mathrm{mix}}^{\mathrm{pc}}(\varepsilon)< t_{\mathrm{mix}}^{\mathrm{cl}}(\varepsilon)$ for all$q\ge3$ and $\varepsilon\in(0,1/2]$. Exact enumeration and$10^{3}$ Monte-Carlo trajectories per start state corroborate the lineardependence on $(q-1)$ and display a constant-factor gap consistent withtheory. The four-cycle thus serves as a transparent test-bed showingwhen path coupling outperforms classical coupling and suggesting metricchoices for larger colouring chains.
1:10 PM – 1:30 PM 120-AB Short Communications

Endo-Reduced Modules Exhibiting Von Neumann Regularity

Strongly regular rings are von Neumann regular with no nonzero nilpotent elements. Various notions of von Neumann regularity for modules, including endo-regularity and F-regularity, have been studied. Recently, endo-reduced modules have been introduced as modules whose endomorphism rings have no nonzero nilpotent elements. In this talk, we study endo-reduced modules exhibiting von Neumann regularity. We show that an endo-reduced, endo-regular module is Abelian endo-regular and, equivalently, an endo-reduced module that is both $P$-flat and $P$-injective. Finally, we show that endo-reduced strong F-regularity unifies several module-theoretic characterizations of strongly regular rings.
1:10 PM – 1:30 PM 118-C Short Communications

Properly Colored Pancyclicity in Edge-Colored Multigraphs with Given Degrees

A $c$-edge-colored multigraph is a multigraph such that each edge is colored with one of the $c$ available colors and no two parallel edges have the same color. A properly colored cycle is a cycle with no consecutive edges having the same color. In this talk, we will discuss sufficient color degree conditions for the existence of Hamiltonian cycle in edge-colored multigraphs, in which between any pair of vertices there are at most $c-1$ parallel edges. Furthermore, we will discuss whether, under the same color degree conditions, it is possible to ensure that the graph is properly pancyclic, as Bondy's metaconjecture states.
1:10 PM – 1:30 PM 118-AB Short Communications

Regularity Results for Two-Phase Free Boundary Problems for Non-Standard Growth Equations with Right Hand Side

Non-standard growth PDEs constitute a broad class of singular and degenerate nonlinear equations used in the modeling of inhomogeneous and anisotropic media. Their applications range from modern material science to image restoration and temperature sensor design.We will present recent results on two-phase free boundary problems governed by operators with non-standard growth. We focus on viscosity solutions to free boundary problems for nonlinear elliptic PDEs with non-zero right hand side and obtain regularity results for solutions and their free boundaries.More precisely, under suitable flatness assumptions we prove that free boundaries are $C^{1,\gamma}$.In addition, we obtain the Lipschitz continuity of viscosity solutions without relying on a monotonicity formula.The interest in these problems stems from the diverse applications that motivate their study and from the challenging difficulties they pose due to their singular / degenerate nature.This is joint work with Fausto Ferrari (University of Bologna, Italy).
1:10 PM – 1:30 PM 119-AB Short Communications

Solution of Stochastic Beltrami Equation with One and with Several Complex Variables

Beltrami differential equation plays an important role in differentareas of mathematics. Let \(D\) be a domain in the complex plane\(\mathbb{C}\), and let \(\mu:D \rightarrow \mathbb{C}\) be a measurable function with \(\left| \mu(z) \right| < 1\) a.e. Beltrami equation is a complex partial differential equation of the form\(f_{\overline{z}} = \mu(z)f_{z}\). Conditions for the existence and uniqueness of solutions for the Beltrami equation are expressed in terms of maximal dilatation and bounded and final mean oscillation. We introduce a stochastic element in the Beltrami equation using stochastic processes with bounded mean oscillation and solve the equation with one complex variable using rough path techniques and local monodromy representations. For solution with several complex variables we refer to presently developing area of holomorphic differential geometry and study the properties and value distribution of our differential operator in \(\mathbb{C}^{n}\). Stochastic differential equations with (one or several) complex variables are a large and important void in the literature in probability theory and mathematics in general and we provide an important research step in this area. We discuss extensions to Painlevé and Schwartzian stochastic equations.
1:10 PM – 1:30 PM 115-B Short Communications

Study of Semi-Geometric Sequences

STUDY OF SEMI-GEOMETRIC SEQUENCESJEAN J. RAKOTO and HANITRINIAINA S. G. RAVELONIRINAAbstract. In this work, we study semi-geometric sequences and spe-cial semi-geometric sequences, focusing on their general term, recurrencerelations, sums of consecutive terms, and convergence behavior. These se-quences originate from the study of Ehrhart polynomials and counterexam-ples to a conjecture proposed by Beck et al. Our analysis provides explicitformulations and convergence criteria for these sequences, highlighting theirrole in discrete geometry and their potential applications in various fieldssuch as evolutionary theory, epidemiology, finance, and mathematical mod-eling
1:15 PM – 2:15 PM Benjamin Franklin Stage Receptions & Special Events

The Proof in the Code: A Conversation with Author Kevin Hartnett & Publisher Thomas Lin

How do we know with complete certainty if something is true? This question looms large even, or especially, in mathematics, where proofs can grow dizzyingly long and abstract, or in generative AI models that cannot distinguish between fact and fiction.

Enter the computer program Lean, the latest in the centuries-long series of attempts to build a “truth oracle,” which has the potential to revolutionize how math is done. Kevin Hartnett, the author of the new book The Proof in the Code and Quanta Books publisher Thomas Lin will discuss the birth and rise of Lean; the future of how mathematicians work, collaborate, and assess truth; and the existential question: Can computers reveal universal truths?

Learn more about this session. 

 

 

1:30 PM – 1:50 PM 115-C Short Communications

Adversarial Generalization of Unfolding (Model-Based) Networks

Unfolding networks are interpretable networks emerging from iterative algorithms, incorporate prior knowledge of data structure, and are designed to solve inverse problems like compressed sensing, which deals with recovering data from noisy, missing observations. Compressed sensing finds applications in critical domains, from medical imaging to cryptography, where adversarial robustness is crucial to prevent catastrophic failures. However, a solid theoretical understanding of the performance of unfolding networks in the presence of adversarial attacks is still in its infancy. In this paper, we study the adversarial generalization of unfolding networks when perturbed with $l_2$-norm constrained attacks, generated by the fast gradient sign method. Particularly, we choose a family of state-of-the-art overaparameterized unfolding networks and deploy a new framework to estimate their adversarial Rademacher complexity. Given this estimate, we provide adversarial generalization error bounds for the networks under study, which are tight with respect to the attack level. To our knowledge, this is the first theoretical analysis on the adversarial generalization of unfolding networks. We further present a series of experiments on real-world data, with results corroborating our derived theory, consistently for all data. Finally, we observe that the family's overparameterization can be exploited to promote adversarial robustness, shedding light on how to efficiently robustify neural networks.
1:30 PM – 1:50 PM 120-AB Short Communications

Hypernorms and Bounded Operators in Hypervector Spaces

A hyperoperation generalizes the notion of a binary operation by allowing the composition of two elements to yield a set rather than a single element. Extending this idea, Al-Tahan and Davvaz introduced hypervector spaces over hyperfields as a generalization of vector spaces over fields. In this work, we study linear and weak linear transformations on hypervector spaces and obtain results on their isomorphisms. We introduce the concept of a hypernorm on a hypervector space and provide illustrative examples. Results on open maps and quotient spaces are established. We examine the structure and completeness of the set of all bounded operators on hypervector spaces and investigate sequences of bounded linear operators in complete hyper Banach spaces.
1:30 PM – 1:50 PM 119-AB Short Communications

On the Hamilton-Jacobi Approach to Mean-Field Spin Glasses

Spin glasses, though originating in statistical physics as models of disordered magnetic systems, have had a remarkable influence across many scientific disciplines. Their key features—frustration, disorder, complex energy landscapes, and multiple metastable states—make them valuable metaphors and analytical tools in diverse fields. For mean-field spin glass models, it is known that the limit of the free energy can be written as the supremum of a functional, this is the celebrated Parisi formula. In this talk, we will discuss the links that exist between this formula and a certain Hamilton-Jacobi equation in Wasserstein space. Using those links, we will derive uniqueness results for maximizers of the Parisi formula for models with scalar and vector spins. This is based on joint work with Hong-Bin Chen and Jean-Christophe Mourrat.
1:30 PM – 1:50 PM 116-A Short Communications

Optimality Conditions Based on the Fréchet/Limiting Second-Order Subdifferentials

In this talk, we present some new results on second-order optimality conditions for minimization problems, where the objective functions are assumed to be $C^{1}$-smooth/$C^{1,1}$-smooth. For doing so, we apply the concept of Fréchet/limiting second-order subdifferentials from variational analysis to the Lagrangian function of the problem under investigation. Our results extend and refine several existing ones.
1:30 PM – 2:30 PM 117-A Roundtable / Panel

Panel on Collaborative Research in Mathematics in Germany: Opportunities and Challenges

Germany’s Clusters of Excellence represent one of the most ambitious funding instruments for cutting-edge research worldwide. In mathematics, several large consortia bring together leading researchers across a wide spectrum of pure and applied fields, supported with an average of 5.5 million euros per Cluster per year (without overhead allowance). These Clusters receive funding for seven years, they are dynamic research ecosystems designed to strengthen Germany’s international visibility, foster innovation, and set new standards in the training of early-career researchers as well as in equality and diversity.

But what does collaborative research of this scale actually mean for mathematics?

This minisymposium takes a closer look at the transformative potential — and the structural challenges — of large-scale collaboration in our discipline, which has led, among other things, to the internationalization of doctoral and postdoctoral programs, making Germany a global hub for mathematical research. Researchers actively engaged in Clusters of Excellence will reflect on their experiences: How has working within a collaborative network reshaped their research questions, methods, and perspectives? What intellectual impulses and formative moments have emerged? Where do synergies truly arise — and where do tensions remain?

Beyond individual perspectives, we will also hear from members of decision-making bodies to better understand the specific opportunities and constraints that collaborative research structures create for mathematics as a field.

By bringing together scientific, strategic, and personal viewpoints, this session aims to spark an open and forward-looking discussion on the future of collaborative research in mathematics.

Panelists:
Alexandra Carpentier, Universität Potsdam
Dominik Maeder, DFG
Katharina Proksch, DFG
Katrin Tent, Universität Münster
Ulrike Tillmann, University of Oxford

1:30 PM – 1:50 PM 118-AB Short Communications

Recent Progress on the Inverse Scattering Theory for Ideal Alfv\'en Waves

The Alfv\'en waves are fundamental wave phenomena in magnetized plasmas. Mathematically, the dynamics of Alfv\'en waves are governed by a system of nonlinear partial differential equations called the magnetohydrodynamics (MHD) equations. Let us introduce some recent results about inverse scattering of Alfv\'en waves in ideal MHD, which are intended to establish the relationship between Alfv\'en waves emanating from the plasma and their scattering fields at infinities. The proof is mainly based on the weighted energy estimates. Moreover, the null structure inherent in MHD equations is thoroughly examined, especially when we estimate the pressure term.
1:30 PM – 1:50 PM 115-B Short Communications

Self-Dual Representations of Metaplectic SL(2)

Let $F$ be a non-Archimedean local field of characteristic zero and $G=\mathrm{SL}(2,F)$. Let $\widetilde{G}=\widetilde{\mathrm{SL}}(2,F)$ be the metaplectic double cover of $G$. Let $\pi$ be an irreducible smooth genuine self-dual generic representation of $\widetilde{G}$. We will discuss an analogue of a result of Dipendra Prasad for the sign of $\pi$. This is a joint work with Ila Ahmad, Sanjeev Kumar Pandey and Varsha Vasudevan.
1:30 PM – 1:50 PM 118-C Short Communications

Some Combinatorial Approaches to the Nonexistence of Iterative Roots

An iterative root of order $n\ge 2$ of a self-map $f$ on a nonempty set is a self-map $g$ on the set such that $g^n=f$. Most existing results on the iterative roots of continuous interval maps rely on tools such as the Intermediate Value Theorem and the monotonicity of bijections. Extending these results to higher dimensions or more general topological spaces is generally complex. In this talk we present some new combinatorial ideas that lead to new results on iterative roots of maps on arbitrary sets and continuous maps on topological spaces. These results, in particular, allow us to generalize some notable findings on iterative roots for continuous interval maps to the broader context of continuous multidimensional maps. The talk is based on two recent joint works with B. V. Rajarama Bhat.
1:30 PM – 1:50 PM 115-A Short Communications

Transient Analysis of a M/M/1 Feedback Queueing System with Differentiated Vacations, Waiting Server, and Balking

This paper investigates a single-server $M/M/1$ feedback queueing system incorporating differentiated server vacations, a waiting server mechanism, and customer balking behavior. Customer arrivals follow a Poisson process with rate $\lambda$, while service times are exponentially distributed with rate $\mu$. Upon service completion, a customer either re-enters the system at the end of the queue with probability $p$ or departs permanently with probability $q$, where $p+q=1$, thereby introducing a feedback structure that captures repeat service requirements.\\After the completion of a busy period, the server does not immediately take a vacation but instead remains idle for an exponentially distributed waiting time with rate $\zeta$. If no arrivals occur during this period, the server initiates a type-I vacation, returning immediately once at least one customer is detected. However, if the system is still empty upon return, the server subsequently takes a shorter type-II vacation. The duration of type-I and type-II vacations are assumed to be exponentially distributed with parameters $\gamma_{1}$ and $\gamma_{2}$, respectively. Customer admission behavior depends on the server’s state: arriving customers always join the queue when the server is busy, whereas during server vacations they join with probability $\beta$ or balk with probability $1-\beta$.\\Using probability generating function techniques and Laplace transform methods, explicit expressions for the system size distribution and several key transient performance measures are derived. The analytical results provide insight into the effects of feedback, vacation differentiation, and balking on system congestion and delay characteristics. The model is applicable to practical service systems such as communication networks, call centers, and healthcare operations, where repeated service, server unavailability, and customer impatience play a significant role.
2:00 PM – 6:00 PM Hall E - Expo Math Festival

Math Festival Day 2

Join us in Hall E for a family-friendly Math Festival open to the public. This interactive celebration of mathematics will feature hands-on activities, engaging talks, games and art designed to inspire curiosity and showcase the beauty and creativity of math for all ages. Discover how mathematics connects to everyday life, science, and culture while experiencing the excitement of one of the world’s largest gatherings of mathematicians.

MathHappens Activity Area

  • Multi-station interactive math playground featuring puzzles, tiles, and tactile models that encourage exploration, pattern recognition, and informal learning through hands-on discovery.

Maze Mat / Twist-n-Roll / Ring of Fire

  • Dynamic large-scale interactive math installations including floor-based mazes, tactile exhibits, and collaborative builds designed for full-body engagement and high visitor throughput.

Probability Power / Clothesline of Chance

  • Interactive game-show style probability experience where participants engage in live challenges (coin flipping + probability ranking) to build intuition around chance and real-world likelihood (close line).

Interactive Math Festival

  • Large-scale hands-on math festival environment featuring multiple table-based activities designed to spark curiosity, collaboration, and joyful problem-solving for K–8 audiences.

Are We There Yet? An Exploration of Distance

  • Immersive multi-model math exploration combining physical builds, interactive puzzles, and VR to demonstrate different concepts of distance and geometry across mathematical systems.

Math Card Game Exhibit

  • Interactive math card game experience connecting middle school math concepts to real-world scenarios through collaborative, play-based problem solving.

Sierpinski Simplices

  • Collaborative fractal-building activity where participants construct a large Sierpinski tetrahedron through hands-on assembly, illustrating patterns, scaling, and mathematical structure.
3:00 PM – 3:45 PM 116-A Section Lecture

Causal Structure and Representation Learning with Biomedical Applications

Massive data collection holds the promise of a better understanding of complex phenomena and, ultimately, better decisions. Representation learning has become a key driver of deep learning applications, as it allows learning latent spaces that capture important properties of the data without requiring any supervised annotations. Although representation learning has been hugely successful in predictive tasks, it can fail miserably in causal tasks including predicting the effect of a perturbation/intervention. This calls for a marriage between representation learning and causal inference. An exciting opportunity in this regard stems from the growing availability of multi-modal data (observational and perturbational, imaging-based and sequencing-based, at the single-cell level, tissue-level, and organism-level). We outline a statistical and computational framework for causal structure and representation learning motivated by fundamental biomedical questions: how to effectively use observational and perturbational data to perform causal discovery on observed causal variables; how to use multi-modal views of the system to learn causal variables; and how to design optimal perturbations.
3:00 PM – 3:45 PM 118-AB Section Lecture

Geometric Characteristics of Observable Regions

Observability is one of the main research areas in control theory. Different forms of observability inequalities not only correspond to different control phenomena but also have their own mathematical meanings. For evolutionary partial differential equations (PDEs), looking into the geometric characteristics of their observable sets/regions is one of the key parts in studying the corresponding observability inequalities. However, research in this area is still far from well understood. In this paper, we first present four distinct observability inequalities within the framework of abstract evolution equations, together with their corresponding control problems. Then, for several specific evolution equations (such as wave equations, heat equations, Schrödinger equations, among others), we provide the definitions of observable sets/regions corresponding to the aforementioned inequalities. Subsequently, we review some existing results and main research methods concerning the geometric characteristics of these observable sets/regions. Finally, we outline several open problems related to the geometric characteristics of observable (and weakly observable, etc.) sets/regions.
3:00 PM – 3:45 PM 115-A Section Lecture

Hard Lefschetz Phenomena and Lie Algebra Actions

I will present several instances where interesting vector spaces, such as cohomologies of moduli spaces, exhibit a symmetry sometimes called the curious hard Lefschetz property. Alongside this, there is an action of a commutative algebra, and it is natural to ask how the two structures interact. In our examples, this interaction gives rise to an action of an explicit Lie algebra. A well-studied case is the geometric Satake correspondence, while recent developments reveal the same pattern in the cohomologies of character varieties, moduli spaces of Higgs bundles, and braid varieties, as well as in the homologies of knots and certain bigraded modules from combinatorics. For the moduli space of Higgs bundles on an algebraic curve, the relevant algebra is the Lie algebra of Hamiltonian vector fields on the plane, yielding the P=W conjecture as a corollary. We conclude with a construction of a candidate module over this Lie algebra, conjecturally isomorphic to the cohomology of the stable twisted Higgs bundle moduli space on the projective line.
3:00 PM – 6:00 PM 117-A IMU Panel

IMU International Commission on the History of Mathematics Symposium

This session invites contributions that examine how mathematical knowledge has been established, communicated, and accepted across historical contexts, with particular attention to the interrelated roles of proof, demonstration, and persuasion. Rather than treating proof as a fixed or universal standard, the session foregrounds the historically contingent practices, norms, and epistemic values that have shaped what has counted as an adequate or convincing demonstration in different mathematical cultures.

Topics may include the historical evolution of standards of demonstration; the diagrammatic, procedural, and rhetorical means by which mathematical arguments have been made persuasive; and the roles of individuals, texts, instruments, and institutions in legitimizing mathematical claims. Contributions may range from ancient and medieval cultures of inquiry to early modern and modern mathematical practice and may engage with diverse epistemic traditions and contexts.

The session also welcomes work that reflects on the relationship between formal proof and other modes of mathematical reasoning, including explanation, visualization, approximation, and heuristic argument. By attending to how demonstration and persuasion have functioned within historical communities, this session aims to illuminate the dynamic interplay between mathematical rigor, communicative practice, and epistemic authority.

 

3:00 PM – 3:45 PM 118-C Section Lecture

Instability, Non-Uniqueness, and Unpredictability in Fluid Equations

In the last 20 years, there have been remarkable progress in understanding non-uniqueness of solutions to the fundamental partial differential equations of incompressible fluid dynamics, namely, the Euler and Navier-Stokes equations. They stem from different viewpoints: just to mention a few, they include convex integration, instability in self-similar variables, numerical evidences. The talk will provide an overview of these developments, focussing on our current understanding of the linear instability of the equations in connection with their nonuniqueness.
3:00 PM – 3:45 PM 120-AB Section Lecture

Many-Body Asymptotics for The Toda Lattice

The Toda lattice prescribes the evolution of N particles interacting under certain Hamiltonian dynamics; it is an archetypal example of a completely integrable system. A question of interest is to understand how the model behaves, under random (or typical) initial data, when the number N of particles becomes large. In this talk describe several results explaining such asymptotics under certain invariant initial data. The proofs proceed by finding a way to interpret the Toda lattice as a dense collection of "quasi-particles" that behave similarly to solitons, and providing a framework to study how these quasi-particles asymptotically evolve in time. In this analysis, arguments from random matrix theory, particularly the analysis of Lyapunov exponents governing the decay rates of eigenvectors of random tridiagonal matrices, play an important role.
3:00 PM – 3:45 PM 122-AB Section Lecture

Mixed Non-Abelian Hodge Theory and the Linear Shafarevich Conjecture

For a complex algebraic variety X, classical Hodge theory imposes extra structure on the singular cohomology Hk(X,C) of X using the theory of harmonic forms.  Non-abelian Hodge theory similarly enriches the geometry of the algebraic variety of representations of the fundamental group (which is thought of as H1(X,GLr(C))) by using harmonic metrics on local systems.  The theory in the "pure" case of smooth projective X was largely worked out in the 1990s beginning with the seminal work of Simpson and has seen many applications, for example the proof of Eyssidieux--Katzarkov--Pantev--Ramachandran of the linear Shafarevich conjecture for such X.  In this talk, I will survey recent advances in the "mixed" case of arbitrary complex algebraic varieties X, and show how these tools can be used to prove a number of important results about the topology of algebraic varieties, as well as a general version of the linear Shafarevich conjecture.

3:00 PM – 5:00 PM Terrace Ballroom Roundtable / Panel

Panel: AI for Mathematics

AI has the potential to transform mathematical research practices. After surveying some notable recent uses of AI in mathematical research, we will turn to broader questions. How can mathematicians acquire experience with and information about these tools? Which disruptions to mathematical research practices should  the community welcome and which disruptions should we resist? What norms might help guide mathematical interactions with AI systems in the realms of theorem proving, paper writing, refereeing, and evaluation? How do we best support junior researchers in their mathematical development while adapting to a rapidly changing future? How do we leverage this technology to advance human understanding of mathematics while centering the values and aesthetics of human mathematicians?

Moderator: Emily Riehl, John Hopkins University

Panelists: 

  • Matthew Ballard, University of South Carolina
  • Bogdan Georgiev, Google DeepMind
  • Javier Gomez-Serrano, Brown University
  • Terence Tao, University of California, Los Angeles
  • Geordie Williamson, University of Sydney

 

3:00 PM – 3:45 PM 115-C Roundtable / Panel

Roundtable: Communicating Mathematics in (Physical & Virtual) Public Spaces

Math! Everywhere! How can schools, families, and communities work together to make math fun, meaningful, and valuable for every child? We will share how families, educators, and local businesses are engaging in playful math learning through MathTrails and the Math! Everywhere! app, reflecting on the role of community partnerships in bridging mathematical understanding, and how digital and physical tools can build ecosystems of math learning that extend beyond the classroom to spark curiosity and confidence in children's everyday math journeys.

3:00 PM – 4:30 PM Benjamin Franklin Stage Receptions & Special Events

Sports Analytics Panel

From the dugout to the sidelines, numbers are changing the way games are played, coached, and won. This panel brings together leading analytics experts from Philadelphia’s professional sports teams to explore how mathematics and data drive decision-making across baseball, basketball, football, hockey, and soccer.

Panelists will discuss how statistical analysis shapes player evaluation, game strategy, and long-term organizational planning—translating complex math into competitive advantage on the field. Whether it’s optimizing lineups, forecasting performance, or finding hidden value in data, this conversation will reveal how math has become an essential tool in sports.

Panelists:

  • Alex Nakahara, Senior Director of R&D, Phillies
  • Ian Anderson, Director of Strategy & Analytics, Philadelphia Flyers
  • Fan-Hal Koung, Assistant General Manager, Philadelphia 76ers
  • Addison Hunsicker, Senior Manager, Soccer analytics at Philadelphia Union soccer
  • James Gilman, Senior Director of Football Research and Strategy  at Philadelphia Eagles football

Moderator: Jordan Ellenberg

Learn more by clicking here. 

3:00 PM – 3:45 PM 119-AB Section Lecture

Thresholds

I will discuss threshold phenomena for increasing properties under product measure, focusing on three related directions. The Kahn-Kalai conjecture, now resolved, compares the threshold of an increasing family with its expectation threshold up to a logarithmic factor. I will describe this result and its fractional relaxation, where spread measures provide a useful dual language. I will then turn to two open directions: the “second” Kahn--Kalai conjecture for graph containment, which asks whether the abstract expectation threshold can be replaced by the graphic expectation threshold, and Talagrand’s discrete convexity conjecture, whose reformulation via k-thresholds leads to graph decomposition questions.

3:00 PM – 3:45 PM 115-B Section Lecture

Towards Bridging The Gap Between Data-Driven and Theoretical Turbulence Closures in Stratified Flows

Developing turbulence closures remains one of the most challenging problems in fluid dynamics. Turbulence closure models are essential for solving the equations of motion in realistic systems, where fully resolving all relevant scales of motion is computationally infeasible. The Navier–Stokes equations, when filtered to isolate large-scale motions, introduce new terms representing the influence of subgrid-scale turbulent stresses. These terms, which can only be computed directly by resolving the turbulence itself, therefore lead to the closure problem: we must add new equations or introduce assumptions to relate the unresolved scales of motions to the resolved flow. Here we consider the closure problem for oceanic flows, i.e., stratified, Boussinesq, incompressible on a rotating frame of reference. In particular, we focus on a closure for ocean mesoscale eddies, which have horizontal scales of 10-100km and are key to the redistribution of momentum, energy, and tracers in the ocean. In particular, mesoscale eddies can reinject energy and momentum into the large-scale flow through an inverse energy cascade. Specifically, we will explore a range of ocean mesoscale closures - theoretical and data-driven - and explore their connection using analysis and data-driven methods. This talk aims to bridge the gap between novel methods in AI and machine learning and theoretical fluid dynamics to address significant challenges in the physics of turbulence.
3:00 PM – 3:45 PM 121-AB Section Lecture

Virtual Fibring of Manifolds and Groups

One can learn a lot about a compact manifold if one can show that it fibres over the circle - in essence, this allows us to view a static n-dimensional manifold as a manifold of dimension n-1 that evolves in time.Being fibred (over the circle) is a relatively rare property. It is much more common to be virtually fibred, that is, to admit a finite cover that is fibred. For example, it was the content of a conjecture of William Thurston, now two theorems by Ian Agol and Dani Wise, that all finite-volume hyperbolic 3-manifolds are virtually fibred; in fact, this property is extremely common among irreducible 3-manifolds.The situation is less clear in higher dimensions. On the obstruction side, we know that virtually fibred manifolds must have vanishing Euler characteristic. This immediately shows that compact hyperbolic manifolds in even dimensions will not be virtually fibred. A more involved obstruction comes from L2-homology: virtually fibred manifolds must be L2-acyclic.The motivation behind the research I will present lies in trying to find situations in which the vanishing of L2-homology is is not only necessary, but also sufficient for virtual fibring. It turns our that a lot more can be said if we replace aspherical manifolds by their homological cousins: Poincare duality groups. Concretely, if G is an n-dimensional Poincare-duality group over the rationals, and if G satisfies the RFRS property, then G is L2-acyclic if and only if there is a finite-index subgroup G0 of G and an epimorphism from G0 onto the integers such that its kernel is a Poincare-duality group over the rationals of dimension n-1. (This last theorem is joint with Sam Fisher and Giovanni Italiano.)The RFRS property was introduced in Agol's work on Thurston's conjecture. A countable group is RFRS if and only if it is residually {virtually abelian and poly-Z}. All compact special groups in the sense of Haglund-Wise satisfy this property, so there is a ready supply of RFRS groups, also among fundamental groups of hyperbolic manifolds in high dimensions.
4:00 PM – 4:45 PM 115-A Section Lecture

BPS Cohomology in Geometry and Representation Theory

We motivate and survey the theory of BPS invariants of categories and BPS cohomology of stacks, indicating applications in enumerative geometry and representation theory, as well as recent advances.
4:00 PM – 4:45 PM 115-B Section Lecture

Differential Stochastic Variational Inequalities and Optimization

The variational inequality (VI) provides a broad unifying setting for the study of equilibrium problems and optimization. The differential variational inequality and stochastic variational inequality are generalizations of the VI and promising modeling paradigms when dynamics and uncertainties are involved in data analysis and decision making. We first discuss the mathematical formulations and recent results of the differential VI and stochastic VI. Next we introduce the differential stochastic VI with stochastic optimization (DSVIO), an ordinary differential equation whose right-hand side is defined by a stochastic VI and solutions of several stochastic optimization problems. The DSVIO provides a powerful modeling framework for various applications in data science and artificial intelligence. We provide sufficient conditions for the existence of a solution pair for the DSVIO in the space of absolutely continuous functions and the space of measurable functions. We discuss a convergent sample average approximation and time-stepping discretization scheme for numerical solutions of the DSVIO. Finally, we show applications of the DSVIO for optimizing multimodal large model-based embodied intelligence systems for the elderly mobility.
4:00 PM – 4:45 PM 116-A Section Lecture

Estimation in Linear High Dimensional Hawkes Processes: A Bayesian Approach

In this paper we study the frequentist properties of Bayesian approaches in linear high dimensional Hawkes processes in a sparse regime where the number of interaction functions acting on each component of the Hawkes process is much smaller than the dimension. We consider two types of loss function: the empirical L1 distance between the intensity functions of the process and the L1 norm on the parameters (background rates and interaction functions). Our results are the first results to control the L1 norm on the parameters under such a framework. They are also the first results to study Bayesian procedures in high dimensional Hawkes processes.

4:00 PM – 4:45 PM 122-AB Section Lecture

Holomorphic Foliations with Numerically Trivial Canonical Bundle

The lecture will survey what is currently known about the structure of holomorphic foliations with canonical singularlities and numerically trivial canonical bundle on projective manifolds.
4:00 PM – 4:45 PM 119-AB Special Joint Section Lecture

Intersection Cohomology Without Spaces

Intersection cohomology categorifies important algebraic and combinatorial polynomials in a number of settings, notably classical Kazhdan-Lusztig polynomials of Coxeter groups, g-polynomials of polytopes, and Kazhdan-Lusztig polynomials of matroids. In each case, there is a special subclass for which the coefficients of the polynomials are equal to local intersection cohomology Betti numbers of certain algebraic varieties: Weyl groups with Schubert varieties, rational polytopes with toric varieties, and realizable matroids with arrangement Schubert varieties. But the formulas for these polynomials make sense for general Coxeter groups, polytopes, and matroids, even though there are no corresponding varieties. In each case, one can give a purely algebraic construction of graded vector spaces whose Poincaré polynomials are equal to these polynomials, thus proving that the coefficients are non-negative. In this talk, we give a survey of some of these constructions, with an emphasis on the matroid case.
4:00 PM – 4:45 PM 118-AB Special Section Lecture

Machine Learning, PDEs and Control

Traditional applied mathematics provides a natural framework for understanding several of the fundamental mechanisms underlying modern Artificial Intelligence. 

In this talk, we will show how control notions and methods, such as simultaneous and ensemble controllability, shed light on the classification and representation capabilities of deep neural networks, leading to an interpretation of learning as a control problem.

The second part of the talk will focus on generative AI. We will show how classical diffusion processes and their associated partial differential equations provide a mathematical perspective on modern generative models, revealing generation as a controlled reversal of heat flow.

Finally, we will address the use of neural networks as computational tools for the approximation of complex systems. In this context, new phenomena emerge, including situations in which physical states converge while the corresponding network parameters escape to infinity, revealing a gap between the well-posedness of the underlying mathematical problem and that of its neural parametrization.

These examples illustrate how control theory, partial differential equations, probability, approximation theory, and scientific computing are becoming increasingly intertwined in shaping the mathematical foundations of AI. They also point toward significant mathematical challenges, both in understanding modern AI and in adapting these methodologies to specialized scientific, engineering, and biomedical applications.

4:00 PM – 4:45 PM 121-AB Section Lecture

Manifolds and Disc-Presheaves

In this talk we explain an approach to the study of smooth manifolds which compares them to presheaves on a category of discs, also known as embedding calculus. We highlight recent work that shows this approach has many desirable properties, as well as recent applications demonstrating its strength
4:00 PM – 5:00 PM Hall E - Expo Poster Presentations

Poster Exhibition

"A coupled PDE–ODE system with boundary interaction arising in heat transfer" by Le Duc Nhien (10 - Partial Differential Equations)

"Transition Matrices Between Permutation Characters of the Symmetric Group and Classical Bases" by Beth Anne Castellano (13 - Combinatorics)

"Algorithms and Criteria for Constructing Ternary Totally Parastrophic-Orthogonal Quasigroups" by Iryna Fryz (13 - Combinatorics)

"Bent partitions, LP-packings, and amorphic association schemes" by Tekgül Kalayci (13 - Combinatorics)

"Chromatic Numbers of Abelian Cayley Graphs" by Mike Krebs (13 - Combinatorics)

"Generalized Chip Firing and Critical Groups of Arithmetical Structures on Trees" by Joel Louwsma (13 - Combinatorics)

"Expansions Among Non-Tensor Bases of Polysymmetric Functions" by David Martinez (13 - Combinatorics)

"A Method for Constructing D-Distance (anti)magic Graphs" by Anak Agung Gede Ngurah (13 - Combinatorics)

"Constructible twin-sets in distance-hereditary graphs" by Martín Safe (13 - Combinatorics)

"On Regular Ramsey \((mK_2, H)\)-Minimal Graphs and Their Extensions" by Kristiana Wijaya (13 - Combinatorics)

"Some Aspects of Probability Related to the Riemann Hypothesis" by Andrey Feuerverger (3 - Number Theory)

"Modular Symmetries and Identities for Rank-Type Partition Statistics" by Rishabh Sarma (3 - Number Theory)

"Infinite tensors meet model theory" by Alessandro Danelon (4 - Algebraic and Complex Geometry)

"Conductor-Discriminant Inequality for Tamely Ramified Cyclic Covers of the Projective Line" by Connor Stewart (4 - Algebraic and Complex Geometry)

"A Simplified Rotation Algorithm of a Vector in Three Dimensions" by Sanji Sun (4 - Algebraic and Complex Geometry)

"The spin Dolbeault-Dirac operator on the quantum Grassmannian $Gr(2,4)$." by Fredy Diaz Garcia (7 - Lie Theory and Generalizations)

"The classification of right alternative and noncommutative Jordan superalgebras" by Abror Khudoyberdiev (7 - Lie Theory and Generalizations)

"Besov Spaces and Statistical Properties of the Shift" by Pedro Augusto da Silva Morelli (9 - Dynamics)

"Hyperbolicity and Hausdorff Measures for Renormalization of Dissipative Gap Mappings" by Márcio Gouveia (9 - Dynamics)

"Large Deviations and Applications in Homogeneous Dynamics" by Taehyeong Kim (9 - Dynamics)

"Spectral Decomposition and Skew-Product for Group Actions" by Keonhee Lee (9 - Dynamics)

"Smoothness, Tangency and Uniqueness of Horospherical Foliations of Geodesic Flows" by Edhin Mamani (9 - Dynamics)

"A Discrete-Time Nonlinear Phytoplankton-Zooplankton Model with Toxin Release" by Sobirjon Shoyimardonov (9 - Dynamics)

4:00 PM – 5:00 PM Hall E - Expo Poster Presentations

Poster Presentation by Author

"A coupled PDE–ODE system with boundary interaction arising in heat transfer" by Le Duc Nhien (10 - Partial Differential Equations)

"Transition Matrices Between Permutation Characters of the Symmetric Group and Classical Bases" by Beth Anne Castellano (13 - Combinatorics)

"Algorithms and Criteria for Constructing Ternary Totally Parastrophic-Orthogonal Quasigroups" by Iryna Fryz (13 - Combinatorics)

"Bent partitions, LP-packings, and amorphic association schemes" by Tekgül Kalayci (13 - Combinatorics)

"Chromatic Numbers of Abelian Cayley Graphs" by Mike Krebs (13 - Combinatorics)

"Generalized Chip Firing and Critical Groups of Arithmetical Structures on Trees" by Joel Louwsma (13 - Combinatorics)

"Expansions Among Non-Tensor Bases of Polysymmetric Functions" by David Martinez (13 - Combinatorics)

"A Method for Constructing D-Distance (anti)magic Graphs" by Anak Agung Gede Ngurah (13 - Combinatorics)

"Constructible twin-sets in distance-hereditary graphs" by Martín Safe (13 - Combinatorics)

"On Regular Ramsey \((mK_2, H)\)-Minimal Graphs and Their Extensions" by Kristiana Wijaya (13 - Combinatorics)

"Some Aspects of Probability Related to the Riemann Hypothesis" by Andrey Feuerverger (3 - Number Theory)

"Modular Symmetries and Identities for Rank-Type Partition Statistics" by Rishabh Sarma (3 - Number Theory)

"Infinite tensors meet model theory" by Alessandro Danelon (4 - Algebraic and Complex Geometry)

"Conductor-Discriminant Inequality for Tamely Ramified Cyclic Covers of the Projective Line" by Connor Stewart (4 - Algebraic and Complex Geometry)

"A Simplified Rotation Algorithm of a Vector in Three Dimensions" by Sanji Sun (4 - Algebraic and Complex Geometry)

"The spin Dolbeault-Dirac operator on the quantum Grassmannian $Gr(2,4)$." by Fredy Diaz Garcia (7 - Lie Theory and Generalizations)

"The classification of right alternative and noncommutative Jordan superalgebras" by Abror Khudoyberdiev (7 - Lie Theory and Generalizations)

"Besov Spaces and Statistical Properties of the Shift" by Pedro Augusto da Silva Morelli (9 - Dynamics)

"Hyperbolicity and Hausdorff Measures for Renormalization of Dissipative Gap Mappings" by Márcio Gouveia (9 - Dynamics)

"Large Deviations and Applications in Homogeneous Dynamics" by Taehyeong Kim (9 - Dynamics)

"Spectral Decomposition and Skew-Product for Group Actions" by Keonhee Lee (9 - Dynamics)

"Smoothness, Tangency and Uniqueness of Horospherical Foliations of Geodesic Flows" by Edhin Mamani (9 - Dynamics)

"A Discrete-Time Nonlinear Phytoplankton-Zooplankton Model with Toxin Release" by Sobirjon Shoyimardonov (9 - Dynamics)

4:00 PM – 4:45 PM 115-C Roundtable / Panel

Roundtable: Mathematics Education in the Advent of the AI Era

As artificial intelligence becomes embedded in education, much discussion has focused on what students can produce with AI or how it can automate assessment and feedback. Yet mathematics is defined as much by process as by product. Its essence lies in conjecturing, reasoning, reflecting, and persisting through uncertainty. Drawing on research in the science of learning, this presentation explores what it means to keep the human at the centre of mathematical learning in an AI-mediated world. It highlights the importance of metacognitive awareness, emotional regulation, and the attitudes that sustain curiosity and persistence in the face of challenge.

Our research on mathematics anxiety shows how performance-oriented environments can undermine these processes, reducing confidence and willingness to explore. Learning to learn mathematics in an AI world means refocusing education on how students think, feel, and make sense of ideas, not only on what they can produce.

4:00 PM – 4:45 PM 118-C Special Section Lecture

Soliton Resolution at Blow-Up for the Subconformal Nonlinear Wave Equation

We consider the nonlinear wave equation (NLW) with a superlinear pure power nonlinearity in the subconformal or conformal cases. Under some conditions on initial data, this equation is known to have solutions which blow up in finite time. Two questions are then relevant: (i) the classification of all possible blow-up behaviors; (ii) the construction of examples of blow-up solutions. As we will show, the situation is entirely settled in the one-dimensional case, where we fully solve the famous ``Soliton Resolution Conjecture''. Various extensions to higher dimensions and to perturbed versions of (NLW) are given, including the construction of a solution in 2-d, with a nearly pyramidal blow-up graph. Carrying out this program was possible thanks to a synergy of techniques from the PDE theory, Mathematical Physics and Analysis, including ODE techniques, spectral theory and energy methods. All over this presentation, we will insist on connections with the study of other types of PDEs, in particular in the parabolic case. Surprisingly enough, in spite of the difference between parabolic and hyperbolic equations at the linear level, the nonlinear nature brings in a strong unity - both in the results and in the methods - between these two important classes of PDEs.
4:00 PM – 4:45 PM 120-AB Special Section Lecture

The Strong Convergence Phenomenon

A family of random matrices is said to converge strongly to a limiting family of operators if the operator norm of every noncommutative polynomial of the matrices converges to that of the limiting operators. Recent developments surrounding the strong convergence phenomenon have led to new progress on important problems in random graphs, geometry, operator algebras, and applied mathematics, while the discovery of new methods has made it possible to establish strong convergence in challenging situations that were previously out of reach. I will aim to provide an introduction to classical and recent developments in this area.
5:00 PM – 5:45 PM 121-AB Section Lecture

A Calabi-Yau Theorem for Degenerations of Compact Kähler Manifolds

To understand a compact Kähler manifold X, it is often helpful to study its degenerations. The idea of non-Archimedean (n-A) Kähler geometry is to think of such degenerations as (possibly weak) Kähler potentials on an associated n-A space. The n-A Monge-Ampère measure of a degeneration is then supposed to encode how the volume of X distributes as X degenerates. In this talk I will discuss a Calabi-Yau theorem in this setting, first proved in the algebraic case by Sébastien Boucksom and Mattias Jonsson (building on earlier work of Sébastien Boucksom, Charles Favre and Mattias Jonsson), and subsequently proved in the general Kähler case by Pietro Mesquita-Piccione and myself. The proof in the Kähler case relies on properties of big cohomology classes, and is related to the transcendental Morse inequality conjecture of Sébastien Boucksom, Jean-Pierre Demailly, Mihai Păun and Thomas Peternell.
5:00 PM – 5:45 PM 115-B Section Lecture

Complexity of Local Problems

A common theme throughout mathematics and computer science is the desire to rigorously measure the complexity inherent in various problems of interest. Depending on the subject area, different notions of complexity can be proposed, resulting in different complexity hierarchies. It has been recently discovered that for a certain broad class of problems, the notions of their complexity originating in four distinct fields—descriptive set theory, computability theory, distributed computing, and probability theory—are intricately intertwined. An active research direction is to complete the resulting “dictionary” between these areas. I will survey what we currently know about these connections and highlight some of the many open questions that remain.
5:00 PM – 5:45 PM 119-AB Section Lecture

Ergodic and Statistical Properties of Smooth Systems

We survey results on ergodic and statistical properties of smooth systems on manifolds that preserve a smooth measure. We will recall some classical results and describe more recent developments. We will also discuss open problems.
5:00 PM – 5:45 PM 118-C Section Lecture

From Stein Manifolds to Oka Manifolds: The H-Principle in Complex Analysis

In this talk, I will describe the main developments in the theory of the h-principle in complex analysis and geometry, better known as the Oka principle. I will present the key notions of Oka manifolds and Oka maps, which developed from the Oka-Grauert principle and Gromov's theory of elliptic complex manifolds and elliptic holomorphic submersions, and their characterization by simpler approximation and ellipticity conditions. I will discuss recent and ongoing developments, open problems, and mention applications to the classical theory of minimal surfaces.
5:00 PM – 6:00 PM Benjamin Franklin Stage Art & Music @ ICM

Mathdramatics: Math on Stage

Math/Theater scholar, Dr. Emma LaPlace, will raise the curtain on plays that put mathematics in the spotlight. Join Dr. LaPlace as she explores how mathematics is portrayed and represented in theatrical productions. Part lecture, part performance, this presentation will bring the scripts to life, and move math from the page to the stage.

Dr. Emma LaPlace is an Assistant Professor of Mathematics at Albertus Magnus College in New Haven, Connecticut, where she also teaches Drama. Her research focuses on the intersection of mathematics and theater. Dr. LaPlace was a double-major in Mathematics and Drama during her undergraduate studies at Vassar College, and earned her PhD from Columbia University. Dr. LaPlace has acted professionally at theaters across Connecticut. Her recent published works can be seen in Mathematical Association of America Focus, and International Journal of Mathematical Education in Science and Technology. She has served as a math/theater consultant, and is currently collaborating with the Conference Board of the Mathematical Sciences for the 2026 Year of Math (you can find her monthly Math on Stage videos on theyearofmath.org). Her Instagram is @mathdramatics.

5:00 PM – 5:45 PM 118-AB Section Lecture

Mathematical and Numerical Analysis of Quantum Signal Processing

Quantum signal processing (QSP) provides a representation of scalar polynomials of degree d as products of matrices in \(\mathrm{SU}(2)\), parameterized by \((d+1)\) real numbers known as phase factors. QSP is the mathematical foundation of quantum singular value transformation (QSVT), which is often regarded as one of the most important quantum algorithms of the past decade, with a wide range of applications in scientific computing, from Hamiltonian simulation to solving linear systems of equations and eigenvalue problems. In this article we survey recent advances in the mathematical and numerical analysis of QSP. In particular, we focus on its generalization beyond polynomials, the computational complexity of algorithms for phase factor evaluation, and the numerical stability of such algorithms. The resolution to some of these problems relies on an unexpected interplay between QSP, nonlinear Fourier analysis on \(\mathrm{SU}(2)\), fast polynomial multiplications, and Gaussian elimination for matrices with displacement structure.
5:00 PM – 5:45 PM 115-A Section Lecture

Pointed Hopf Algebras Revisited, with A View from Tensor Categories

Hopf algebras appear in connection with various problems in Pure Mathematics and Theoretical Physics, mainly through their categoriesof representations, which are examples of tensor categories. In recent years, there have been major advances in the classification of finite-dimensional Hopf algebras over the complex numbers, especially when restricted to the pointed case. In this talk, we will summarize the main results in this direction, stating the classification theorems recently obtained and the problems still open, and describing the tools needed to solve the problem by means of the so-called Lifting Method of Andruskiewitsch and Schneider. An important fact is that the category of comodules of a lifting (under the assumption of the classification theorems) is tensor equivalent to that of the associated graded objects, which in turn allows certain problems to be reduced to the associated graded pointed Hopf algebras. We will emphasise this point of view with applications to other contexts related, such as finite pointed tensor categories, Hopf algebras that do not satisfy the Chevalley property and their finite-dimensional Nichols algebras, and finally module categories over the categories of representations of pointed Hopf algebras.
5:00 PM – 5:45 PM 115-C Roundtable / Panel

Roundtable: Teaching Math in Multilingual Spaces

5:00 PM – 5:45 PM 122-AB Section Lecture

The Accumulating Remainder Tree and Its Impact in Number Theory

The accumulating remainder tree (ART) is a device that has played an increasingly pivotal role in large-scale computations involving a variety of number-theoretic topics. These range from elementary number theory, such as searching for Wilson primes or counterexamples to Kurepa's conjecture, to deeper problems such as studying generalisations of the Sato--Tate conjecture for abelian varieties over number fields. For all of these tasks, the ART leads to algorithms that run in (average) polynomial time, an enormous improvement over previous exponential-time methods. In this talk, I will explain how the ART works, discuss a number of examples of its use in the literature, and consider prospects for future applications.
5:00 PM – 5:45 PM 116-A Section Lecture

The Future of Prediction: in Conversation with Oskar Morgenstern

A century ago, economist Oskar Morgenstern studied what he called one of the most central and most difficult problems in the theory of prediction: predictions that actively influence outcomes. Self-fulfilling and self-negating prophecies are two extreme cases of a fundamental problem that arises with all predictions about social outcomes. People act on predictions in ways that change the course of events, a phenomenon called performativity. Morgenstern argued that performativity doomed prediction in the social world to guesswork with unforeseeable results. This talk gives an entry point to the emerging area of performative prediction that provides counterpoints to Morgenstern's pessimistic prophecy. The standard formulation of machine learning as risk minimization assumes a fixed data-generating distribution. Performative prediction extends risk minimization toward data-generating distributions that depend on the predictive model. This extension leads to the powerful algorithmic principle of repeated risk minimization, alternating risk minimization and model deployment indefinitely. Under suitable conditions, repeated risk minimization converges to a stable point, a kind of equilibrium at which the predictive model minimizes risk on the distribution it entails. We'll discuss three perspectives on performativity using ideas from economic modeling, optimization, and the theory of forecasting that contribute principled ways to reason about predictions that influences outcomes.
5:00 PM – 5:45 PM 120-AB Section Lecture

The Quest for A Classification of 2D Quantum Phases of Matter

Quantum information ideas and techniques are playing an increasing role in the study of quantum many body systems. We will review some recent results in this direction and discuss their relevance within the current program to give a mathematical classification of topological quantum phases of matter in 2D quantum spin systems. We will also describe some of the ideas and techniques behind the proofs.
5:30 PM – 6:30 PM Terrace Ballroom Public Lecture

Between Numbers and People: The Art of Mathematical Communication

Mathematics shapes the modern world, from medicine and climate science to technology and public policy. Yet too often, it remains invisible or inaccessible to the very communities it serves. To meet the challenges of the future, mathematicians must not only discover new knowledge, but also learn to share it in ways that inspire curiosity, trust, and participation. In this talk, Talithia Williams will explore how storytelling can transform the way we communicate mathematics to the public. By connecting ideas to human experience, culture, and purpose, we can turn abstract concepts into meaningful narratives that invite people into the joy of discovery.
6:00 PM – 6:45 PM 118-AB Section Lecture

Compatible Numerical Schemes for Thermodynamically Compatible Systems of Hyperbolic Partial Differential Equations

In this contribution two recent types of compatible numerical discretizations for overdetermined, thermodynamically compatible systems of hyperbolic partial differential equations (PDE) are discussed. Overdetermined hyperbolic and thermodynamically compatible (HTC) systems satisfy an additional extra conservation law for the total energy density, which is a consequence of all the other equations and which corresponds to the first principle of thermodynamics. The second principle of thermodynamics is contained in the entropy inequality, if present in the governing PDE system under consideration. Very often, such systems are also endowed with stationary differential constraints (involutions), such as the divergence-free condition of the magnetic field in the Maxwell equations or the curl-free condition of the velocity field in the equations of linear acoustics. Preserving at least one of the two aforementioned additional structural properties of the governing PDE system exactly at the discrete level is the major objective of the present paper. The first type of numerical schemes achieves compatibility with the extra conservation law for the total energy for a very general class of nonlinear hyperbolic PDE systems, but does not satisfy additional stationary differential constraints. The second scheme is compatible with the extra conservation law and preserves involutions exactly at the discrete level, but only for a very particular class of problems. The design of compatible numerical schemes for general nonlinear hyperbolic systems which satisfy both structural properties at the same time is still the subject of ongoing and future research.
6:00 PM – 6:45 PM 121-AB Section Lecture

Complexity of Submanifolds, Mean Curvature and Singularities

I will survey some recent developments in mean curvature flow and minimal submanifold theory related to understanding the simplest singularities of these geometric variational problems. This is linked with broader questions about quantifying the complexity of submanifolds.
6:00 PM – 6:45 PM 120-AB Section Lecture

Holography and Mathematics

Holography and the Large N Expansion are important ideas in Theoretical Physics: they establish a bridge between Quantum Field Theory, Quantum Gravity and String Theory. The recent formulation of simplified models of Holography leads to conjectural identifications between systems which admit a rigorous mathematical definition. It should thus be possible to formalize and prove such conjectures, and perhaps use them to guide a formalization of String Theory. I will discuss the Large N Expansion from a categorical perspective and illustrate some rigorous or potentially rigorous examples of Holography.
6:00 PM – 6:45 PM 119-AB Section Lecture

Measure Rigidity Beyond Homogeneous Dynamics

We describe recent work that extends some of the measure and topological rigidity results in dynamical systems from situations homogeneous under a Lie group to quite general manifolds.
6:00 PM – 6:45 PM 118-C Section Lecture

Restricted Orthogonal Projections

Projection theorems study how Hausdorff dimension of fractal sets behaves under orthogonal projections from Euclidean space to its subspaces. We will survey some of the recent results on orthogonal projections to restricted families of subspaces and their connections to restriction theory in harmonic analysis and incidence geometry in combinatorics.
6:00 PM – 6:45 PM 116-A Section Lecture

Spreadness and Mixing: A New Strcture vs Randomness Refinement

The classical structure vs. randomness paradigm decomposes an object into a structured component and a random-looking remainder. This method has seen several applications in combinatorics and graph theory from Roth and Szemerédi to modern regularity methods. Recent works introduced a refined viewpoint based on "spreadness" and "mixing". This perspective has led to substantial improvements for several problems, including: (i) upper bounds for 3-term arithmetic-progression-free sets, (ii) explicit separations of deterministic and randomized communication in the three-player Number-On-Forehead model, and (iii) a spread regularity lemma with algorithmic consequences for triangle detection and Boolean matrix multiplication, and (iv) the corners problem. I will survey these developments.
6:00 PM – 6:45 PM 115-A Section Lecture

Totally Positive Toeplitz Matrices: Classical and Modern

The subject of upper-triangular totally positive Toeplitz matrices turns out to be a rich one, relating in the infinite case to the infinite symmetric group and its representations (classical theory), and in the finite case to flag varieties and their quantum cohomology rings (modern). We describe the asymptotics of the modern theory and tropicalise both to uncover a third relation, to the parametrisation of Lusztig's canonical basis.
6:00 PM – 6:45 PM 115-B Section Lecture

Towards a First-Order Quantum Logic? A Few Thought on Continuous Logic, Affine Logic, and What's Between Them.

From a practical point of view, continuous first-order logic provides us with a framework for the model-theoretic study of metric structures.  From a more abstract point of view, it also raises quite naturally the question of what should non-commutative continuous logic be?

This is an intentionally vague question that lends itself to more than one interpretation.  One way to understand it is to observe that the algebra of continuous formulas forms (the self-adjoint part of) a commutative, unital C*-algebra.  Can we drop « commutative » here?  What should that even mean?

Ideas coming from recent developments in affine logic finally allow us to propose an answer to this question, giving rise to a logic that is strongly reminiscent of the Dirac--von Neumann formalism for observables in quantum mechanics.

 

7:00 PM – 9:00 PM Marriott Grand Ballroom Receptions & Special Events

American Mathematical Society Reception

Join the American Mathematical Society for an evening of conversation and community. Explore AMS membership, programs, publications, and resources that support mathematicians at every stage of their careers. Enjoy light refreshments as you build new connections and celebrate the global mathematical community.

Open to all ICM attendees

Sunday, July 26, 2026

9:00 AM – 10:00 AM Terrace Ballroom Plenary Lecture

Dynamics and Rigidity Through the Lens of Circles

We report on recent developments in the dynamics and rigidity of infinite-volume homogeneous spaces through the lens of circles. By addressing four natural questions about circle packings, we highlight the interplay between dynamics, geometry, and rigidity that defines the emerging frontier of homogeneous dynamics.
9:00 AM – 6:00 PM Hall E - Expo Expo and Collaborations

Exhibition & Collaboration

10:15 AM – 11:15 AM Terrace Ballroom Plenary Lecture

Random Matrices: Wigner Universality, Anderson Delocalization, and Beyond

In this lecture, we review developments in random matrix theory, with an emphasis on progress over the past two decades. The guiding principle is Wigner's universality thesis, which asserts that the spectral statistics of highly correlated systems resemble those of classical random matrix ensembles. Anderson's localization--delocalization transition for the tight-binding model extends this vision to non-mean-field models. The main results covered in this lecture include the resolution of the Wigner--Dyson--Mehta conjecture, the Sarnak--Miller--Novikoff--Sabelli conjecture on Ramanujan graphs, and delocalization and universality for band matrices and block Anderson models in all dimensions.

We begin by reviewing the three-step strategy for establishing universality in mean-field random matrices and the obstacles to extending this strategy to non-mean-field ensembles. We then outline a new method based on the loop hierarchy and its tree approximation, which yields quantum diffusion. Finally, we explain how quantum diffusion modifies the three-step strategy and leads to proofs of universality for non-mean-field models.

10:30 AM – 10:50 AM 115-B Short Communications

Analytical Modeling of Foam Flow with Nanoparticles in Porous Media

Foam injection techniques have become increasingly relevant for controlling gas mobility in subsurface applications such as CO$_2$ storage, enhanced oil recovery, and environmental remediation. A central challenge in these processes is maintaining foam stability under reservoir conditions. Recent studies indicate that the addition of nanoparticles can substantially improve foam resistance and overall performance. Despite growing experimental evidence, there is a lack of analytical investigations.In this work, we develop new mathematical models describing nanoparticle-stabilized foam flow in porous media. The first model assumes foam in local equilibrium and is described by a non-strictly hyperbolic system of conservation laws. We prove existence and uniqueness of a global solution of the associated Riemann problem, which consists of sequences of shock, rarefaction, and contact waves. The analytical solution provides a rigorous basis for investigating macroscopic quantities related to sweep efficiency.The second model accounts for bubble population balance through a source term describing foam generation and destruction, and incorporates nanoparticle retention leading to permeability reduction. This yields a more complex, nonconservative formulation. By exploiting the structure of the resulting system of ordinary differential equations, we derive a semi-analytical steady-state solution. The model captures two competing retention mechanisms (viscosity enhancement and permeability loss) and demonstrates mathematically that neglecting one or both effects leads to systematic underestimation of pressure.
10:30 AM – 10:50 AM 120-AB Short Communications

Discretization of Conformally-Invariant Dirac-Like Operators in 3D via Natural Differential Operations, and Applications to Geometric Inverse Problems

Although a well-developed notion of natural differential operators in the context of the deRham complex has existed since the 1950s, it is only recently that a similar notion has been developed in the context of triangulations of manifolds embedded in ${R}^n$ and connected to the deRham complex in a functorial manner. In Riemannian geometry, conformally invariant differential operators are associated with the middle dimension of an even-dimensional manifold, and there is no linear counterpart on odd-dimensional manifolds. In this paper we summarize the construction of a nonlinear elliptic Dirac operator on 3-dimensional manifolds with boundary, the variational formulation, and Whitney form discretization, with an emphasis played by the role of discrete differential operations. This formulation is then applied to highly nonconvex inverse problems. Primarily, isotopy classes of near force-free magnetic fields characterized by contact structures and the Giroux correspondence.
10:30 AM – 10:50 AM 118-C Short Communications

On Some Common Fixed Point Results Under New Compatibility

Metric space clearly forms a natural environment for exploring fixed points of single and multivalued mappings. The fixed point theory as a part of non-linear analysis is a study of function equation in metric or non-metric settings. It provides necessary tools for the existence of theorems in non-linear problems. The classical Banach contraction principle in metric space is one of the fundamental results with wide applications. Among several generalized forms of metric space, the study of common fixed point of mappings in a fuzzy metric space satisfying certain contractive conditions has been at the center of vigorous research activities. Also, the role of compatible mappings for the existence of common fixed point is very crucial. The notion of compatible mappings of type (K) in metric space was introduced by K. Jha, V. Popa and K.B. Manandhar in 2014. The objective of this talk is to discuss some common fixed results for self-mappings in some generalized forms of metric space under this new compatible mappings which generalizes and improves similar results of fixed points.
10:30 AM – 10:50 AM 118-AB Short Communications

Optimality Conditions for Minimax and Maxmin Problems

Minimax and maxmin problems have an important role in optimization, global optimization, game theory, and operations research. The classical minimax theorem of von Neuman deals with the equality conditions of maxmin and minimax values. In a generalcase, since the maxmin and minimax values are not always equal, therefore, the optimality conditions for both problems might be different. In this talk, we formulate new optimality conditions forthe minimax and maxmin problems. Illustrative examples are given for the problems
10:30 AM – 10:50 AM 115-A Short Communications

Partial Order in Module Over a Matrix Nearring and a Group Nearring

The notion of partial order plays a significant role in studying concepts such as positive elements, convex ideals, and ordered morphisms in algebraic systems. In this presentation, we introduce a partial order on modules over a nearring and explore its connections with matrix nearring. Due to the absence of one of the distributive properties in nearrings (compared to rings), the structural aspects of partial orders in nearrings and matrix nearrings become especially significant. We establish a characterization of the positive cone in a group nearring, analogous to the positive cone in a matrix nearring. Furthermore, we examine properties of convex ideals and the conditions associated with Archimedean orders in both matrix nearrings and group nearrings. These results give new developments into the structure of ordered nearrings.
10:30 AM – 10:50 AM 115-C Short Communications

Rademacher-Type Exact Formula and Higher Order Tur\'{a}n Inequalities for Cubic Overpartitions

In 1918, Hardy and Ramanujan made a breakthrough by developing the circle method to deduce an asymptotic formula for the partition function p(n), which was later refined by Rademacher in 1937 to produce an absolutely convergent series representation for p(n). Since then, Rademacher-type exact formulas for various partition functions have been investigated by many mathematicians. The concept of overpartitions was introduced by Lovejoy and Corteel in 2004. Kim, in 2010, studied an overpartition analogue of cubic partitions, termed as cubic overpartitions. The main objective of this paper is to establish a Rademacher-type exact formula for cubic overpartitions and, as an application, to derive an explicit error term that leads to their log-concavity. Furthermore, applying a result of Griffin, Ono, Rolen, and Zagier, we establish higher-order Tur\'{a}n inequalities for cubic overpartitions. In addition, we obtain log-subadditivity and generalized log-concavity properties for cubic overpartitions inspired by the work of Bessenrodt-Ono and DeSalvo-Pak on the ordinary partition function.
10:30 AM – 10:50 AM 116-A Short Communications

Rigidity Results for Serrin’s Overdetermined Problems in Riemannian Manifolds

In this lecture, we are interested in studying Serrin’s overdetermined problems in Riemannian manifolds. For manifolds endowed with a conformal vector field, we prove a Pohozaev-type identity to establish a Serrin-type rigidity result using the P-function approach introduced by Weinberger. To achieve this, we proceed with a conformal change, starting from a geometric identity due to Schoen. Moreover, we obtain a symmetry result for the associated Dirichlet problem by utilizing a generalized normalized wall shear stress bound.
10:30 AM – 10:50 AM 119-AB Short Communications

The Rest of the Tilings of the Sphere by Regular Spherical Polygons

Determining the set of tilings of the sphere by regular polygons is a problem that dates back to the time of the ancient Greeks. For edge-to-edge tilings, it was completed in 1967. Here, we discuss recent results that finish the problem by determining all non-edge-to-edge tilings of the sphere by regular polygons. This is joint work with Cameron Edgar, Peter Hollander and Liza Jacoby.
10:50 AM – 11:10 AM 119-AB Short Communications

A Coding - Theoretic Characterization of Intron Regions in DNA Sequences

DNA sequences consist of gene regions known as exons and introns. Exon regions are spliced and directly participate in protein synthesis, whereas intron regions are non-coding segments that are excluded from this process. In our previous work, we introduced a novel coding-theoretic model for the mathematical representation of genomic regions and validated its effectiveness on a limited dataset. In the present study, we extend this model by proposing an improved version of the algorithm and by conducting a comprehensive evaluation on a significantly larger dataset. The proposed algorithm models DNA segments as algebraic codes and examines their structural parameters, with particular emphasis on error-correction properties.Our results reveal that genomic regions corresponding to introns are consistently mapped to algebraic codes with zero error-correction capability. This outcome provides a mathematically precise criterion for distinguishing non-coding regions and demonstrates that algebraic invariants from coding theory offer a robust analytical tool for genomic classification.***Acknowledgements:The author Elif Segah OZTAS would like to acknowledge the contribution of the COST Action CA21169, supported by COST (European Cooperation in Science and Technology).
10:50 AM – 11:10 AM 118-AB Short Communications

An EPQ Model for Electronics Industry to Determine Optimal Scheduling Times

The consumer electronics industry operates in a highly dynamic environment, characterized by rapid technological advancements, short product lifecycles, and intense market competition. Effective production scheduling is paramount for manufacturers to minimize operational costs and sustain profitability. Traditional inventory models often fall short in capturing the unique complexities of this sector, particularly concerning the swift onset of product obsolescence and the necessity for dynamic pricing strategies. This paper introduces an extended Economic Production Quantity (EPQ) model specifically designed to address above challenges within the electronics manufacturing context by mathematical modelling of an inventory system characterised by : (1) price difference dependent demand, (2) constant rate of production, (3) inventory level dependent selling price, and (4) non- instantaneous deterioration . The primary objective is to determine optimal production starting and stopping times that minimize the total system cost per unit time. The comprehensive total cost function considers setup, production, holding, deterioration (obsolescence) costs, shortage, and sustainability costs (e.g., related to production emissions). The mathematical model distinguishes between two critical scenarios based on the timing of obsolescence relative to production completion: Case 1, where obsolescence begins after production stops, and Case 2, where obsolescence starts during or before production ceases. The objective function is formulated using differential equations to describe inventory levels across various time intervals. MATHEMATICA 12.0 Software is employed to solve the complex system of non-linear equations derived from differentiating the total cost function, thereby obtaining the optimal scheduling policies.By providing a robust framework for optimizing production schedules under these realistic and industry-specific conditions, this research offers valuable managerial insights. It assists electronics manufacturers in effectively managing inventory depreciation due to obsolescence, mitigating shortage risks, and making informed pricing decisions in a highly competitive and dynamic market. The inclusion of sustainability costs further enhances the model's relevance for modern, responsible manufacturing practices, paving the way for more efficient and environmentally conscious supply chain management in the electronics sector.
10:50 AM – 11:10 AM 115-A Short Communications

Complexity, Curvature and Homological Dimension of Modules Under Linkage

In this article, we analyze how (projective and injective) complexity, curvature, and complete intersection dimension behave under linkage of modules and ideals. Let $R$ be a Gorenstein local ring. Consider a Gorenstein perfect ideal $\mathfrak{a}$ (e.g., $\mathfrak{a}$ is generated by an $R$-regular sequence). Let $M$ and $N$ be two Cohen-Macaulay $R$-modules linked by $\mathfrak{a}$. We prove that ${\rm cx}_R(M) = {\rm injcx}_R(N)$ and ${\rm curv}_R(M) = {\rm injcurv}_R(N)$. In particular, when $R$ is complete intersection, ${\rm cx}_R(M) = {\rm cx}_R(N)$ and ${\rm curv}_R(M) = {\rm curv}_R(N)$. Furthermore, we show that projective dimension ${\rm pd}_R(M)={\rm pd}_R(N)$, and complete intersection dimension ${\rm cid}_R(M)={\rm cid}_R(N)$. If any of these dimensions is finite, it is equal to height of $\mathfrak{a}$. Similar results are obtained for linkage of ideals. All these results highly extend a classical result of Peskine and Szpiro in many directions. We construct several examples that complement our results. These also show how properties like `integrally closed', `$\mathfrak{m}$-full' and `Burch' behave under linkage of ideals. This is a joint work with Subhadip Bhowmick.
10:50 AM – 11:10 AM 115-C Short Communications

Distributions of Prime Truncations

The prime number 357686312646216567629137 is notable because of the unusual property that it remains prime successively on removing the left digit until there are no remaining digits. In this talk we will explore the more general phenomena of the distribution of the number of prime truncations of integers and irreducible truncations of polynomials with coefficients over a finite field. This is joint work with Vivian Kuperberg.
10:50 AM – 11:10 AM 115-B Short Communications

Martingale Roblem for Two-Dimensional Stochastic Heat Flow

We consider a two-dimensional time-fractional stochastic differential equation\[\begin{equation*}\partial^{\alpha}_{0t}u(t,x)=\frac{1}{2}\Delta u(t,x)+\lambda u(t,x)\dot{W}(t,x), t>0,x\in R^{2},\end{equation*}\]where $\partial^{\alpha}_{0t}$ - Caputo fractional derivative order $\alpha$, $0 < \alpha\leq 1,$ $\dot{W}$- white noise in $[0,\infty)\times R^{2},$ $\lambda$ is the noise intensity coefficient. Using the idea of Bertini - Cancrini we consider the regularized system of equations \[\begin{equation}\partial^{\alpha}_{0t}u^{\beta_{0},\beta_{\varepsilon}}(t,x)=\frac{1}{2}\Delta u^{\beta_{0},\beta_{\varepsilon}}(t,x)-\beta_{\varepsilon} u^{\beta_{0},\beta_{\varepsilon}}(t,x)\dot{W}(t,x), t>0,x\in R^{2},\end{equation}\]where $\beta_{0}\geq 0$ and $\beta_{\varepsilon}$ defined as $$\beta_{\varepsilon}=\sqrt{\frac{2\tau}{-log\varepsilon}+\frac{\rho+O(1)}{(-log\varepsilon)^{2}}}, \ \ \rho \in R.$$It was proved that, if the initial function $u(0,x)=u_{0}(x)\in L^{2}(R^{2}), \psi\in L^{2}(R^{2)$. Then the variation$<\displaystyle{\int_{R^{2}}} u^{\beta_{0}, \beta_{\varepsilon}}(t,x)\psi(x)dx>_{t}$ converges to some random variable when $\varepsilon\rightarrow 0.$Thus, the density of the the random field from (1) is found. Moreover, it is proved that the higher order moments are finite, so, the field of the random point should be a random field. Finally, the weak convergence of the random field is proved for the case of directed polymers. Thus, the solution of equation (1) will be the limit Z represented in the form of $$\int_{R^{2}}Z(t,x)\psi(x)dx-\int_{R^{2}}Z(0,x)\phi(x)\psi(x)dx=$$$$=\frac{1}{\Gamma(1-\alpha)}\int_{0}^{t}(t-s)^{-\alpha}\int_{R^{2}}\frac{1}{2}\Delta Z(s,x)\psi(x)dxds+$$$$+\frac{1}{\Gamma(1-\alpha)}\int_{0}^{t}(t-s)^{-\alpha}\int_{R^{2}}\beta Z(s,x)\dot{W}(dx,ds),$$where $\phi \in C_{c}^{+}(R^{2}), \psi \in C_{b}^{2}(R^{2}). $It has been proved that the stochastic integral in the last term is the martingale and its quadratic variation can be written in terms of Z.Also, the conditions of uniqueness of this martingale were found.
10:50 AM – 11:10 AM 118-C Short Communications

Perturbations of Non-Autonomous Second-Order Abstract Cauchy Problems

In this talk we present time-dependent perturbations of second-order non-autonomous abstract Cauchy problems associated to a family of operators with constant domain. We make use of the equivalence to a first-order non-autonomous abstract Cauchy problem in a product space, which we elaborate in full detail. As an application, we provide a perturbed non-autonomous wave equation. This talk is based on joint work with Christian Seifert (TU Hamburg, Germany).
10:50 AM – 11:10 AM 120-AB Short Communications

Torsion, Curvature and Serret-Frenet's Geometry in Quantum Mechanics

Torsion and curvature associated with quantum states of physical systems are formulated. The proposed exercise presents significant geometric features in the context of Background Independent Quantum Mechanics (BIQM). For the first time torsion in quantum evolution is evaluated by using first principles is found to be precisely equal to the sixth order moments. Now, if the odd order moments and odd order expectation values for symmetric functions are equated to zero, the principal term in the expression of square of torsion is found to have reduced to a concise expression $\tau^2=\frac{\langle H^6\rangle}{\langle H^2\rangle^3}$. Also, square of the curvature is found to be precisely equal to fourth order moments what is known as kurtosis in statistics, whereas, square of torsion is found to be equivalent to the sixth order moments of Hamiltonian of a system. For the perfectly symmetric functions, for which the third order moments known as skewness and odd order expectation values when assumed to be zero, the principal term in the expression of curvature is found be $\kappa^2 \equiv\frac {\langle H^4\rangle}{\langle H^2\rangle^2}$. This verifies the earlier results of Brody and Houghston by estimator approach. Thus, the direct evaluation of curvature and torsion in the framework of Geometry of $Serret-Frenet$ formulae in the context of Geometric Quantum Mechanics bears extremely meaningful results.
10:50 AM – 11:10 AM 116-A Short Communications

When Two Pairwise Comparisons Determine or Bound the Third

Let $\epsilon = P(A>B)$, $\eta = P(B>C)$, and $\zeta = P(C>A)$, where A, B and C are real-valued random variables. It is possible to define a space $(\epsilon, \eta, \zeta)$ under general conditions, and this space is a proper subset of the unit cube. A natural question arises: under what conditions can the third comparison be inferred from the other two?This framework is motivated by clinical trials, where $\epsilon, \eta, \zeta$, represent comparisons of time to death in a cancer trial for treatments $A, B$, $C$. In practice, trials comparing $A$ vs. $B$ and $B$ vs. $C$ exist. However, an additional trial comparing $C$ vs. $A$ is usually not performed. The field of network meta-analysis seeks to estimate these missing comparisons from available trial data. Standard methods in this field assume transitivity, which holds true for univariate statistics such as comparisons of means. However, $P(A>B)$ is a head-to-head comparison and can be non-transitive; that is, $B$ outperforms $A$ and $C$ outperforms $B$ does not imply $C$ outperforms $A$. Thus, for head-to-head comparisons, determining whether it is possible to reliably estimate missing third comparison based on the available data is non-trivial. In this work, we address this problem across several scenarios.Trybula characterized the $(\epsilon, \eta, \zeta)$ space. We show that it is a proper subset of the unit cube. This allows us to bound the unobserved comparison. Additionally, by restricting this space to the Weibull and Gaussian families, two common scenarios in clinical research, we achieve tighter bounds. Hazard ratio (HR) is another head-to-head comparison. HRs are often estimated with Cox regression, which assumes the proportionality of hazards (PH), i.e. the ratio of hazards in two treatment arms is constant. In this work, we prove that the PH assumption implies transitive behavior, HRs are mutually recoverable, and we derive the third HR from the other two. Furthermore, if PH assumption holds, win proportions ($P(X>Y)$=win proportion) are monotonic transformations of HRs, hence the third WP is also recoverable from the other two.Our findings demonstrate that the geometry of the $(\varepsilon,\eta,\zeta)$ space and certain scenarios allow us to bound the unobserved comparison. Extending this approach to other families of distribution functions remains an open direction for future research.
11:00 AM – 1:00 PM Benjamin Franklin Stage Films @ ICM

Margeuritte's Theoreme

Film Directed by Anna Novion

The trajectory of Marguerite’s future, a brilliant Mathematics student at the esteemed Ecole Normale Supérieure, appears meticulously charted. As the sole woman in her cohort, she nears completion of her thesis, anticipating the culmination of years of dedicated effort with an audience of researchers. However, on the crucial day, an unexpected error disrupts her well-laid plans, causing the unraveling of all her certainties and the collapse of her foundational aspirations. Faced with this pivotal moment, Marguerite resolves to abandon her current path entirely and embarks on a journey to redefine and reconstruct her life anew.

Source: MSP FILM

11:10 AM – 11:30 AM 118-AB Short Communications

A Multi-Stage Capacity Expansion Stochastic Model for Power Generation

Bangladesh’s rapid electricity demand growth calls for resilient and cost-effective power expansion planning. This thesis develops a multi-stage stochastic programming model that jointly optimizes generation, transmission, and sub-transmission investments under uncertainties in demand, fuel prices, and renewable output. Renewable capacity factors are generated using Monte Carlo simulation, with scenarios structured into a multi-stage decision tree. Compared with a conventional two-stage model, the proposed approach reduces expected costs by approximately 30%, increases the renewable energy share to nearly 40%, and significantly mitigates load shedding. Sensitivity analyses highlight sub-transmission upgrades and renewable incentives as critical levers. The framework provides planners with a practical and adaptive tool for designing sustainable and flexible power system expansion strategies.
11:10 AM – 11:30 AM 115-C Short Communications

Cyclic Number Fields with Prescribed Elementary Iwasawa Module

For a number field $F$ and a prime number $p$, let $F_{\infty}$ be the cyclotomic ${\mathbb Z}_p$-extension of $F$ and $X_{\infty}(F)$ be the unramified Iwasawa module of $F_{\infty}$, that is the Galois group over $F_{\infty}$ of the maximal abelian unramified pro-$p$-extension. We prove that each finite elementary abelian $p$-group is realizable as $X_{\infty}(F)$, where $F$ runs over an infinite set of cyclic number fields of degree $p$.
11:10 AM – 11:30 AM 115-A Short Communications

Jordan and Lie σ-Derivations on Path Algebras

Lie $\sigma$-derivations on path algebras. Motivated by Benkovič’s works on triangular algebras and by Li and Wei’s studies on derivations of path algebras, we extend these results by removing the faithfulness condition. We establish that every Jordan $\sigma$-derivation on a path algebra associated with a finite acyclic quiver is a $\sigma$-derivation, and every Lie $\sigma$-derivation is of standard form. These findings confirm that, under suitable algebraic constraints, Jordan and Lie $\sigma$-derivations behave analogously to classical $\sigma$-derivations, thus generalizing existing results in algebraic structures connected to quivers and representation theory.
11:10 AM – 11:30 AM 119-AB Short Communications

On Graphs with Maximal Local Distance Antimagic Chromatic Number

Let $G$ be a graph of order $p$ without isolated vertices. A bijection $f: V(G) \to \{1,2,3,\dots,p\}$ is called a local distance antimagic labeling, if $w_f(u)\ne w_f(v)$ for every edge $uv$ of $G$, where $w_f(u)=\sum_{x\epsilon N(u)} {f(x)}$. The local distance antimagic chromatic number $\chi_{lda}(G)$ is defined to be the minimum number of colors taken over all colorings of $G$ induced by local distance antimagic labelings of $G$. In this paper, we present a sufficient condition for a graph $G$ to have $\chi_{lda}(G) = |V(G)|$ and determine some family of graphs $G$ whose $\chi_{lda}(G) = |V(G)|$.
11:10 AM – 11:30 AM 115-B Short Communications

Riemann Problems for Non-Strictly Hyperbolic Systems Arising in Three-Phase Foam Flow

We study the Riemann problem for a system of nonlinear conservation laws arising in the modeling of three-phase flow with foam in porous media. The system is non-strictly hyperbolic due to the presence of an interior umbilic point, where the characteristic speeds of different families coincide, leading to nonclassical wave interactions and difficulties in constructing admissible weak solutions.Assuming foam in local equilibrium, modeled through a constant mobility reduction factor, we analyze a three-phase flow system with large viscosity contrasts. Within this framework, we develop a systematic method to construct Riemann solutions using wave curve analysis, Hugoniot loci, and traveling wave criteria for shock admissibility. This approach enables the classification of solution structures for foamed gas and water injection across a wide range of initial states.The results provide analytical insight into wave interactions near the umbilic point and clarify mechanisms leading to oil bank formation in displacement processes. The analytical predictions are supported by numerical simulations and are relevant to both the qualitative theory of conservation laws and the calibration and validation of numerical solvers used in porous media flow.
11:10 AM – 11:30 AM 116-A Short Communications

Small Area Estimation of Mortality for Countries with Limited and Scarce Data – Nepal as a Case Study

Introduction: Vital Statistics are scarce in developing countries. The system of continuous registration of vital events is not efficient in such countries. Hence there is an urgent need to develop mathematical techniques that address this problem. Data on fertility and migration are scarce. National data on mortality are still scarcer, due to its somber nature. Further mortality data for small places are practically nonexistent. But these data serve as development indicators and provide guidelines to policy makers and planners. The reason behind the sorry state of such data is the lack of awareness, incentives and remote geographical locations. Materials and Methods: This paper is developed keeping this knowledge gap in mortality data into consideration. Life tables explain the mortality experience of a cohort. It is an important component in the computation of average life expectancy at birth and age specific death rates. In this paper, a parsimonious regression model for survivorship function l_x on age and time variables is developed. The inherent pattern of l_x , based on census data from 1971 to 2011 is identified. Results and Discussion: The behavior of the regression coefficients and the model efficiency parameters are analyzed. Then this model is calibrated for small places. The mortality of two small places of Nepal namely, Kathmandu and Manang are estimated. The developed model is validated on the abundant and good quality data of Germany and the state of Niedersachsen. Conclusion: It is said that something is better than nothing. The developed technique and the model discussed here, estimated deficient mortality data with a high degree of accuracy. This was true, not only for developing countries like Nepal and India, but also for developed countries like Germany.
11:10 AM – 11:30 AM 120-AB Short Communications

Warped Products of Dualistic Structures in Information Geometry

Dualistic structures on statistical manifolds are a fundamental concept connecting information geometry, affine geometry and Hessian geometry.Since several statistical manifolds can be seen as warped product spaces, weconstruct dualistic structures on product statistical manifolds based on warped product methods and we give some topological and geometrical conditions under which they induced an Hessian geometry on the statistical manifolds.
11:10 AM – 11:30 AM 118-C Short Communications

Weak Diffeomorphisms for Conservation Laws

Reformulating hyperbolic conservation laws in a Lagrangian form provides an equivalent description of the problem by means of particle paths. Research in this direction was pioneered by Arnold in 1966, who described the dynamics of an ideal fluid as a geodesic flow on the group of volume-preserving diffeomorphisms of a fixed domain. For systems which describe fluid flow, construction of particle paths follows naturally from the associated velocity field. However, the idea of a particle path can be extended to scalar equations and to systems which do not include velocity fields explicitly. In this presentation, we demonstrate how to find a particle path in the form of a weak diffeomorphism, for any scalar conservation law having a smooth flux not necessarily convex, and establish such a particle path as an extremal of a related action functional.
11:30 AM – 11:50 AM 118-AB Short Communications

An Infinite Family of Hyperovals in Polar Spaces of Rank 3

The study of finite projective planes started at the end of the 19th century. The original believe that all such planes were Desarguesian turned out to be false. Hall's coordinatization method laid the foundation for constructing nondesarguesian planes from various algebraic structures such as quasifields, semifields, etc. These algebraic connections turned out to be an impetus in their investigation. Ever since Segre's seminal classification result on ovals in odd order Desarguesian planes, also various substructures of finite planes, such as (hyper)ovals and unitals, were investigated along with their ample applications to other areas such as graph, design and coding theory. There is renewed interest in these substructures, because of their various applications in Ramsey theory, even leading to the solution of a decades-old problem of Erdős by Mattheus and Verstraete. Hyperovals, being sets of points meeting each line in either 0 or 2 points, also played a pivotal role in the computer-assisted nonexistence proof of the projective plane of order 10.Various generalizations to other structures have been considered, such as to polar spaces which are central objects in Tits' theory of buildings. Buekenhout and Hubaut showed that hyperovals in polar spaces are related to extended generalized quadrangles, which provide several geometric models on which classical and sporadic groups act. Although many constructions already existed in the rank 2 case, the situation was quite different for polar spaces of rank 3, where only a handful of small ``sporadic'' examples were known (being found by a computer backtrack search).It is only very recently [1] that the first infinite family of hyperovals in polar spaces of rank 3 was found, more specifically in the Klein quadric by using ovoids of symplectic spaces, resulting in examples that are related to orthogonal and Suzuki groups. These hyperovals are the only known examples of a (potentially) larger family of hyperovals in polar spaces of rank 3. We will discuss this infinite family of hyperovals, their isomorphism problem, and the (ongoing) progress made towards finding additional examples in this larger family.Bibliography[1] B. De Bruyn. An infinite family of hyperovals of Q^+(5,q), q even. J. Combin. Theory Ser A 208 (2024), 105938.
11:30 AM – 11:50 AM 118-C Short Communications

Consequences of Pressure Elimination for Fluid-Structure Interaction Models

In this talk we present applications of our new technique for eliminating and recovering the pressure for a fluid-structure interaction model that is valid in general bounded Lipschitz domains, without additional geometric conditions such as convexity of wedge angles. The specific fluid-structure interaction (FSI) that we consider is a well-known model of coupled Stokes flow with linear elasticity. The coupling between these two distinct PDE dynamics occurs across a boundary interface, with each of the components evolving on its own distinct geometry, and with the boundary interface being Lipschitz. We consider both linear and nonlinear versions of this FSI system (i.e., Stokes and Navier-Stokes flow), where we obtain the well-posedness of the continuous PDE in such general geometries. We illustrate some consequences of our pressure-elimination technique, such as numerical approximations, where it provides FEM convergence estimates over polygonal domains. For the nonlinear case, to deal with the Navier-Stokes and associated boundary nonlinearities we adopt an approximating nonlinear semigroup formulation of a certain truncated problem, and give a new proof of maximality of the associated nonlinear semigroup via a mixed variational form. We illustrate the advantages of our method in a FEM for solutions of the static PDE where the approximating fluid subspace does not require the divergence-free condition.
11:30 AM – 12:30 PM Terrace Ballroom Emmy Noether Lecture

ICM Emmy Noether Lecture: Karen Vogtmann: Moduli Spaces of Graphs

Finite metric graphs represent processes and objects in many different areas of mathematics and science, so one would like to understand the set of all graphs relevant to a given problem, i.e. the moduli space of such graphs.  In this talk I will highlight some recent progress in the study of moduli spaces of graphs, first reviewing historical developments that have led up to them. I will concentrate on moduli spaces of graphs with a specified fundamental group, and explain how the study of such spaces both contributes to and profits from the theory of outer automorphism groups of free groups. Finally, I will mention connections with the classical symmetric space of lattices in Euclidean space, with Kontsevich’s graph complexes and with the algebraic geometers’ moduli space of tropical curves.

The ICM Emmy Noether Lecture honors women who have made fundamental and sustained contributions to the mathematical sciences. The ICM Emmy Noether Lecture is named after the German mathematician Emmy Noether. Since 2006, this lecture is a permanent ICM tradition, since 2014, a special commemorative plaquette is given to each ICM Emmy Noether Lecturer.

11:30 AM – 11:50 AM 120-AB Short Communications

Milnor Spheres via Spherical T-Duality and Generalized Log Transform

In talk we will explore the interplay between Spherical T-duality, exotic spheres, and the generalized log transform, highlighting new connections in geometric topology and complex geometry. Spherical T-duality extends the classical T-duality by replacing the role of the circle group $\mathrm{U}(1)$ with the 3-sphere $\mathrm{S}^3$ or the group $\mathrm{SU}(2)$, relating $\mathrm{SU}(2)$ bundles equipped with degree-7 cohomology cocycles. A remarkable class of examples involves the 7-dimensional homotopy spheres $\Sigma^7$, whose product with $\mathrm{S}^1$ exhibits phenomena such as distinct holomorphic structures transported via spherical T-duality, which contrasts with classical Hopf manifolds like $\mathrm{S}^3 \times \mathrm{S}^1$.Building on this framework, we introduce the generalized log transform, a tool extending classical techniques from 4-dimensional elliptic fibrations to higher-dimensional settings. Applying this to 8-dimensional homotopy Hopf manifolds, we reveal parallels between these constructions and their lower-dimensional counterparts, providing new insights into the role of singularities and complex structures. This is joint work with Leonardo Cavenaghi and Ludmil Katzarkov.
11:30 AM – 11:50 AM 115-A Short Communications

Non-Commuting Graphs of Projective Spaces Over Central Quotients of Lie Algebras

Let $L$ be a finite-dimensional non-abelian Lie algebra with the center $Z(L)$. In this talk, we define a non-commuting graph associated with $L$ as the graph whose vertex set is the projective space of the quotient algebra $L/Z(L)$, and two vertices Span $\{ x + Z(L) \}$ and Span $ \{ y + Z(L) \}$ are adjacent if $x$ and $y$ do not commute under the Lie bracket of $L$. We present several theoretical properties of this graph. For certain classes of Lie algebras, we show that if the non-commuting graphs from two Lie algebras are isomorphic, then these Lie algebras themselves must be isomorphic. Furthermore, we discuss a relation between graph isomorphisms between non-commuting graphs of Lie algebras over finite fields and the size of the algebras.
11:30 AM – 11:50 AM 115-C Short Communications

Non-Principal Euclidean Ideals in Real Biquadratic Fields

In his foundational work, Lenstra introduced the notion of a Euclidean ideal class and showed, under the Generalized Riemann Hypothesis, that for a non-imaginary quadratic number field the existence of a Euclidean ideal class is equivalent to the class group being cyclic. Later, Graves developed a powerful method to prove the existence of Euclidean ideals in more general settings by combining a Motzkin-type lemma with large sieve estimates. Building on these ideas and on subsequent work of Hsu, Chattopadhyay--Muthukrishnan, and Krishnamoorthy--Pasupulati, we study non-principal Euclidean ideal classes in real biquadratic extensions of $\mathbb{Q}$.We consider families of real biquadratic fields $K = \mathbb{Q}(\sqrt{q},\sqrt{d})$,with $q \equiv 3 \pmod{4}$, where the class group $\mathrm{Cl}(K)$ is a $2$-group and its Sylow $2$-subgroup is cyclic. For such fields, we compute the $2$-rank of $\mathrm{Cl}(K)$, describe the (narrow) genus field, and obtain explicit conditions on the ramification and splitting of primes which ensure that the Hilbert genus field is a quadratic extension of $K$. Combining these structural results with a density statement à la Graves for suitable sets of prime ideals, we prove that whenever the class number $h_K$ is a power of two, there exists a non-principal Euclidean ideal class in $K$. We also give many explicit examples obtained with \textsc{PARI/GP} that illustrate the range of applicability of the method.Finally, we discuss how the same strategy can be adapted to other families of real biquadratic fields and how it suggests possible extensions to more general abelian number fields over $\mathbb{Q}$, where the interaction between genus theory, capitulation phenomena, and Euclidean ideal classes remains largely open.
11:30 AM – 11:50 AM 115-B Short Communications

Oscillation of an Impulsive Differential Equations System with Piecewise Constant Argument

In this talk, we investigate existence of oscillatory solutions of a system of impulsive differential equations with piecewice constant arguments. First, we introduce the corresponding difference equation which is the main tool for the investigations. Then sufficient conditions for the oscillation of the solutions are obtained. Moreover, the results are compared with the non-impulsive case. Finally, numerical examples are given to illustrate the validity of the results.
11:30 AM – 11:50 AM 119-AB Short Communications

Proof of Convergence of a Laplace Expansion Algorithm for Calculating Recursions Satisfied by a Family of Determinants

In Evan and Hendel's recent proof of an outstanding conjecture on the resistance distances of a family of linear 3-trees, a key technique in the proof was calculating the recursion satisfied by a family of determinants. The underlying algorithm employed to prove the conjecture converged (i.e. terminated) in the particular case studied, and the paper presented an open question on when such a procedure converges in general. The purpose of this paper is to begin to answer this open question by proving convergence of the procedure for an arbitrary family of determinants of banded, square, Toeplitz matrices. Moreover, the algorithm in this paper modifies the algorithm of Evans and Hendel, improving various aspects of the procedure.
11:30 AM – 11:50 AM 116-A Short Communications

Robust Active Contour Model for Image Segmentation Based on Fractional Order Differentiation

Active contour models based on the level-set framework have gained widespread recognition for their ability to effectively segment a wide range of images. This approach excels in handling complex topology changes during curve evolution while the previous algorithms cannot deal with them. One of the primary benefits of active contour models is their capability to achieve precise segmentation of objects within images, irrespective of their diverse characteristics such as intricate backgrounds, varying shapes, and positions, all without necessitating the training of the model. In this paper, we have introduced a novel approach known as the fractional active contour model, specifically designed to effectively segment images that exhibit noise and inhomogeneity in intensity. To address both noise and inhomogeneity, we have devised a model that seamlessly integrates image denoising and segmentation tasks, enabling us to tackle these challenges simultaneously. The efficacy of our proposed coupled system of partial differential equations, which utilizes fractional order differentiation, has been verified through experiments conducted on clean, noisy, and ultrasound images. The proposed model demonstrates superior performance compared to other existing active contour models, both visually and quantitatively, as evidenced by significant improvements in measures such as Hausdorff distance and the dice similarity coefficient.
11:50 AM – 12:10 PM 115-C Short Communications

A $q$- Series Identity of Uchimura and Its Numerous Generalizations

In 1981, Uchimura rediscovered an interesting $q$-series identity of Ramanujan, whose one side is the generating function for the divisor function $d(n)$. Mainly, he proved the following identity. For $|q|<1$, \[\begin{equation*}\sum_{n=1}^\infty n q^n (q^{n+1})_\infty =\sum_{n=1}^{\infty} \frac{(-1)^{n-1} q^{\frac{n(n+1)}{2} } }{(1-q^n) ( q)_n } = \sum_{n=1}^{\infty} \frac{ q^n }{1-q^n}.\end{equation*}\]Over the years, this identity has been generalized by many mathematicians in different directions. Uchimura himself in 1987, Dilcher (1995), Andrews-Crippa-Simon (1997), and recently Gupta-Kumar (2021) found a generalization. Any generalization of the right most expression of the above identity, we call as divisor-type sum, whereas a generalization of the middle expression we say Ramanujan-type sum, and generalization of the left most expression as Uchimura-type sum. In this talk, we shall discuss these generalizations and present a unified theory. This is joint work with S.C. Bhoria, P. Eyyunni and B. Maji.
11:50 AM – 12:10 PM 116-A Short Communications

A New Shifted Lomax-X Family of Distributions Generated via the T-X Transformation: Properties and Applications to Risk and Financial Data

The modeling of heavy-tailed risks is a central concern in actuarial and financial sciences. In this work, we introduce a new shifted Lomax-X (SHL-X) family of distributions constructed using the T-X transformation, which is known for its capacity to generate flexible distributional structures. Our construction is motivated by the limitations of the classical Lomax distribution in adapting to complex real-world data with skewness and heavy tails. A notable special case, the shifted Lomax-Weibull (SHL-W) distribution, is analyzed in detail. We study the mathematical properties of the SHL-W model, including its moments, quantile function, entropy, and hazard behavior, to provide insight into its structure and potential for practical use. The parameters of the model are estimated using the method of maximum likelihood. Through simulation studies, we assess the performance of the estimators in terms of bias and mean squared error under various sample sizes. To demonstrate practical applicability, the SHL-W distribution is fitted to real insurance claims data. The results show that the new model offers improved goodness-of-fit and tail flexibility compared to traditional models, supporting its use in pricing, risk assessment, and financial modeling. This study contributes a versatile new family of distributions with strong theoretical underpinnings and demonstrable effectiveness in applications where modeling extreme or skewed values is essential.
11:50 AM – 12:10 PM 115-B Short Communications

An Optimal Stock Selling Rule with Constraints

This talk is about an optimal stock selling rule with trading constraints. The goal is determining the time to sell the equity to maximize a discounted reward function. A geometric Brownian motion model represents the underlying stock price movement, and the trading permission process is given in terms of a two-state Markov chain. The optimal policy is determined by a threshold level obtained from solving an associated set of Hamilton-Jacobi-Bellman (HJB) equations (quasi-variational inequalities), from which a closed-form solution is obtained. A verification theorem is provided. Numerical experiments are also included to demonstrate the dependence of the optimal policy and value functions on input parameters.
11:50 AM – 12:10 PM 120-AB Short Communications

Conformally Flat Manifolds with Constant Ricci Scalar

We present characterisations of Lorentzian manifolds with constant Ricci scalar curvature. We study 2-, 3- and 4-dimensional conformally flat Lorentzian manifolds and construct their Ricci scalar curvature in terms of the conformal factor. We do this by solving the relevant (non-linear) partial differential equations. We substantiate our results by providing insightful illustrative examples of our investigation, like the Minkowski space.
11:50 AM – 12:10 PM 118-C Short Communications

Global Well-Posedness of One-Phase Muskat Problem with Surface Tension

We establish the global well-posedness of the one-phase Muskat problem with surface tension for small initial data. This problem describes the motion of the interface separating a wet region from a dry region within a porous medium, a process governed by Darcy’s law. Although physically essential, the inclusion of surface tension introduces an additional challenge. We prove the existence of a unique global strong solution for small initial data. Moreover, if the initial data is periodic, then the solution converges to zero as $t\rightarrow\infty$. To the best of our knowledge, this work constitutes the first global well-posedness result for the one-phase Muskat problem with surface tension. This talk is based on the joint work with Hongjie Dong (Brown University).
11:50 AM – 12:10 PM 118-AB Short Communications

On the Generalizations of Some Fiber Bundles and Their Model Foliations

In this talk I will speak about generalization of somme fiber bundle and their model foliations. \\Let $\psi$ be an Anosov diffeomorphism of the torus $\mathbb T^2$ induced by a matrix $A\in SL(2,\mathbb Z)$ with $|trA|>2$. Consider the $3$-manifold $\mathbb T_A^3$ obtained by suspension of $\psi$. We obtain two codimension-one foliations without compact leaves on this manifold.\\These two foliations are called {\it model foliations.}We generalize this construction as follows? Le $A$ be a matrix $A$ in $SL(2, \mathbb Z)$ which is diagonalizable and the eigenvalues are irrational numbers. We obtain the manifold$\mathbb T_A^{n+1}$ by suspension of the diffeomorphism of the $n-$torus $\mathbb T^n$ induced by the matrix $A$.This manifold fibers over the circle with fiber the $n-$torus $\mathbb T^n.$ We construct two familiesof model foliations which are codimension-$(n-1)$ foliations and codimension-one foliations. We call these foliations respectively the codimension-$(n-1)$ model foliations and the codimension-onemodel foliations on $\mathbb T_A^{n+1}.$ More generaly for $12$ and $\mathbb T_A^3$ the $3-$manifoldobtained by suspension of $\psi$. We define a diffeomorphism of $\mathbb T^2\times [0,1]$ as follows:$$\Psi(x,t)= (\psi(x), t)$$This diffeomorphism descends to the quotient to give a diffeomorphism of $\mathbb T_A^3$ which we denote also by $\Psi.$We define the $4-$manifold $M_A^4$ by suspension of $\Psi$.$$M_A^4=\mathbb T_A^3\times [0,1]/(X,0)\sim (\Psi(X),1).$$$M_A^4$ is a fiber bundle over the circle with fiber $\mathbb T_A^3$.\\We construct by suspension of the model foliationson $\mathbb T_A^3$ by a diffeomorphism of $\mathbb T_A^3$, two codimension-one foliations on $M_A^4$ called model foliations.
11:50 AM – 12:10 PM 119-AB Short Communications

Strong Chromatic Index of Some Graphs

An edge-coloring of a graph $G$ is an assignment of colors to the edges of $G$, with one color assigned to each edge. If adjacent edges are assigned distinct colors, then the edge-coloring is said to be a proper edge-coloring. A strong edge-coloring of a graph $G$ is a proper edge-coloring in which edges at distance at most $2$ receive distinct colors. The minimum number of colors required for a strong edge-coloring of a graph $G$ is called the strong chromatic index, denoted by $\chi_s'(G)$. In this paper, the authors investigate the strong chromatic index of certain special graphs and of the join of two graphs.
11:50 AM – 12:10 PM 115-A Short Communications

Weyl Modules for Lie Superalgeras

The Weyl modules play an important role in the representation theory of infinite-dimensional Lie algebras. However, in super setting the study of Weyl modules has been less developed than the corresponding theory in Lie algebras. Calixto, Lemay and Savage study Weyl modules (global and local) for Lie superalgebras of the form $\mathfrak{g}\otimes_{\mathbb{C}} A$, where A is an associative commutative unital $\mathbb{C}$-algebra and $\mathfrak{g}$ is a basic complex Lie superalgebra or $\mathfrak{sl}(n, n), n \geq 2$. Bagci, Calixto and Macedo studied Weyl modules and Weyl functors for the superalgebras $\mathfrak{g} \otimes A$, where $\mathfrak{g}$ is either $\mathfrak{sl}(n, n), n \geq 2$, or any finite dimensional simple Lie superalgebra not of type $\mathfrak{q}(n)$. We define global and local Weyl modules for $\mathfrak{q} \otimes A$, where $\mathfrak{q}$ is the queer Lie superalgebra and $A$ is an associative commutative unital $\mathbb{C}$-algebra. In this talk, we will discuss global Weyl modules are universal highest weight objects in certain category up to parity reversing functor $\Pi$. Then with the assumption that $A$ is finitely generated, we show that the local Weyl modules are finite dimensional and further they are universal highest map-weight objects in certain category up to $\Pi$.
12:00 PM – 1:30 PM 120-C IMU Panel

IMU Circle of Friends Lunch (Invitation Only)

12:00 PM – 6:00 PM Hall E - Expo Poster Presentations

Poster Exhibition - Part 1

"The Negative Order Modified Korteweg-de Vries Equation with a Self-Consistent Source" by Shoira Atanazarova (10 - Partial Differential Equations)

"Determining Wavenumbers for Hall and Electron Magnetohydrodynamics" by Hassan Babaei (10 - Partial Differential Equations)

"Existence and Uniqueness of Solutions for Loaded Mixed-Type Equation with Fractional Integral Operators" by Yulduz Babajanova (10 - Partial Differential Equations)

"Integration of the Negative Rrder Nonlinear Schr\"odinger Equation with Self-Consistent Source" by Iroda Baltaeva (10 - Partial Differential Equations)

"Uniform Inviscid Damping and Vorticity Depletion Near Non-Monotonic Shear Flows" by Shan Chen (10 - Partial Differential Equations)

"On Local Well-Posedness of the Stochastic Incompressible Density-Dependent Euler Equations" by Claudia Lorena Duarte Espitia (10 - Partial Differential Equations)

"Cauchy Problem for Generalized Euler--Poisson--Darboux Equation with Loaded Term" by Zebo Egamberganova (10 - Partial Differential Equations)

"A Constructible Conductivity Cloak via Homogenisation" by Eleanor Gemida (10 - Partial Differential Equations)

"On an Algorithm for Finding Solutions of Initial–Boundary Value Problem for Functional–Hyperbolic Equation with Distributed Parameters" by Narkesh Iskakova (10 - Partial Differential Equations)

"A Topological Derivative-Based Method to Image Inhomogeneities in an Acoustic Waveguide" by Umid Karimov (10 - Partial Differential Equations)

"A Boundary Value Problem for a Degenerate Elliptic Equation with Singular Coefficients" by Kalligul Kazakbaeva (10 - Partial Differential Equations)

"Geometric Rigidity and Unstable Set Decomposition of Normally Hyperbolic Frozen Waves" by Jihoon Lee (10 - Partial Differential Equations)

"A coupled PDE–ODE system with boundary interaction arising in heat transfer" by Le Duc Nhien (10 - Partial Differential Equations)

"Global Boundedness and Pattern Formation in a Flux-Limited Keller–Segel System with Logistic Growth" by Ruiliang Li (10 - Partial Differential Equations)

"Regime Dependent Infection Propagation Fronts in an SIS Model." by Vahagn Manukian (10 - Partial Differential Equations)

"A Nash Stratification Inequality and Global Regularity for a Chemotaxis-Fluid System on General 2D Domains" by Naji Sarsam (10 - Partial Differential Equations)

"Fractional Sturm–Liouville Problem on Metric Graphs" by Ariukhan Turemuratova (10 - Partial Differential Equations)

"Inverse Problems for Nonlinear Parabolic Equations in Degenerate Domains" by Madi Yergaliyev (10 - Partial Differential Equations)

"Non-Local Problems for the Fractional Order Diffusion Equation and the Degenerate Hyperbolic Equation" by Nargiza Yuldasheva (10 - Partial Differential Equations)

"Discrete Wave Turbulence of a Coupled System of Quintic Schrödinger Equations" by Shayan Zahedi (10 - Partial Differential Equations)

12:00 PM – 6:00 PM Hall E - Expo Poster Presentations

Poster Exhibition - Part 2

"Nonlocal Ordered Mean Curvature with Integrable Kernel" by Animesh Biswas (8 - Analysis)

"On I-Convergence, I-Limit Point and I-Cluster Point of Sequences of Bi-Complex Numbers" by Shyamal Debnath (8 - Analysis)

"On Nonsmooth Global Implicit Function Theorems for Locally Lipschitz Functions from Banach Spaces to Euclidean Spaces" by Guy Degla (8 - Analysis)

"Structure of Projections in algebras generated by n-potent operators" by Priyadarshi Dey (8 - Analysis)

"On the Injectivity of the Spherical Mean value operator" by SAJITH GOVINDAN KUTTY MENON (8 - Analysis)

"Fractional Maps of Generalized Beta Functions and Their Applications to Astrophysical Reaction Rates" by Hussaini Joshua (8 - Analysis)

"Directional Poincaré inequality on compact Lie groups" by Andre Kowacs (8 - Analysis)

"Counterexamples to the Berger–Coburn and Bauer–Coburn–Isralowitz conjectures for Toeplitz operators on Fock space" by Sam Looi (8 - Analysis)

"Perturbation Ideals and Fredholm Theory in Banach Algebras" by Tshikhudo Lukoto (8 - Analysis)

"A Story-Based Introduction to Time Scale Calculus" by Shekhar Singh Negi (8 - Analysis)

"Pseudodifferential Operators on Noncommutative Tori" by Carolina Neira Jimenez (8 - Analysis)

"Some fixed point theorems in strictly convex Menger PM-spaces" by Rale Nikolic (8 - Analysis)

"Directional Maximal Operators and Kakeya-Type Sets" by Blanca Radillo-Murguia (8 - Analysis)

"STABLE CLOSE-TO-CONVEXITY AND RADIUS OF FULL CONVEXITY FOR SENSE-PRESERVING HARMONIC MAPPINGS" by Ankur Raj (8 - Analysis)

"Proportional Calculus and Proportional Differential Equations: Theory and Applications" by Mayuree Sompui (8 - Analysis)

"Spectral Rigidity of Commutators: Dynamical Stability vs Nilpotency" by Hranislav Stanković (8 - Analysis)

"Oblique Dual Frame Completion in Euclidean Spaces: A Product Matrix Approach" by Gino Angelo Velasco (8 - Analysis)

"Construction of Mercedes-Benz Frames via QR Factorization" by Long Wang (8 - Analysis)

"Restriction and Kakeya maximal estimates in Four Dimensions" by Yufei Zhan (8 - Analysis)

"Weighted estimates for some class of quasilinear operators" by Nazerke Zhangabergenova (8 - Analysis)

12:10 PM – 12:30 PM 115-A Short Communications

Extending Free Group Action on Surfaces

We develop a complete invariant for the solution to the following question: Which free actions on oriented surfaces equivariantly bound? the Schur multiplier is divided by toral classes to obtain the Bogomolov multiplier, then a free action of a finite group $G$ over an oriented closed surface $M$ equivariantly bounds, if and only if, the class $[G,M]$ is trivial in the Bogomolov multiplier. We show that free actions always extend in the case of abelian, dihedral, symmetric, and alternating groups. We show extendable actions for Coxeter groups and the analog of non-orientable surfaces and three-manifolds.
12:10 PM – 12:30 PM 115-B Short Communications

Mathematical Modeling and Analysis of Control Measures in Dengue Disease Transmission Dynamics

Mathematical Modeling and Analysis of Control Measures in Dengue Disease Transmission DynamicsGanga Ram PhaijooDepartment of Mathematics, School of Science, Kathmandu UniversityDhulikhel, Kavre, NepalEmail: gangaram@ku.edu.npAbstractDengue disease is a vector-borne disease. It is endemic in tropical and subtropical regions worldwide. The disease is caused by any one of the four serotypes of the dengue virus, which is spread to humans through the bites of the infected Aedes mosquitoes. Several disease-control strategies, which help to bring the disease transmission under control, are introduced in this work. A SEIR-SEI compartmental model is proposed to study the impact of these control measures on the transmission dynamics of the dengue disease. The next-generation matrix method has been used to compute the basic reproduction number, Ro of the model, which serves as a metric to measure persistence of the disease. The disease-free equilibrium of the model is found to be asymptotically stable when Ro<1 and unstable when Ro>1. A sensitivity analysis is performed to identify the model parameters that significantly affect the disease transmission. Numerical simulations are carried out to evaluate the impact of various control strategies on the disease dynamics graphically. The results highlight the importance of the control measures in reducing the value of Ro below unity, thereby achieving effective control in the disease transmission.Keywords: Dengue; Control Measures; Stability; Basic Reproduction Number; Sensitivity Analysis
12:10 PM – 12:30 PM 118-C Short Communications

Pseudo-Anosov-Like Maps on the Infinite Ladder Surface

Let $S_g$ be the closed surface of genus $g$, $\mathcal{L}$ be the infinite Jacob's ladder surface, and $\text{Map}(S)$ denote the mapping class group of a surface $S$. Let $q_g:\mathcal{L}\rightarrow S_g$ be the regular infinite-sheeted cover with deck transformation group $\mathbb{Z}$. In this talk, we show the existence of ``pseudo-Anosov-like" maps on $\mathcal{L}$ that arise as the lifts of Penner-type pseudo-Anosov maps on $S_g$ under the cover $q_g$. Furthermore, we establish that these lifts are topologically transitive, mixing, and support null recurrent dynamics. Moreover, we present concrete examples of infinite families of such maps on $\mathcal{L}$.
12:10 PM – 12:30 PM 115-C Short Communications

Sections of Rational Elliptic Lefschetz Fibrations

We give a list of monodromy factorizations in the pure mapping class group $\rm{PMod}(T^2_{d+1})$ of a torus with $d+1$ marked points that represent all lines (aka rational $(-1)$-curves)on a del Pezzo surface $Y={\mathbb C}P^2\#(9-d)\overline{{\mathbb C}P}^2$ of degree $d$, for $d\leq 3$. These factorizations are lifts of a certain fixed monodromy factorization in $\rm{PMod}(T^2_{d})$ that represents $Y$.In the case $d=1$, which we discuss in more detail, we give an explicit correspondence between the set of such factorizations and the240 roots of $E_8=K^\perp$ (orthogonal complement in $H_2(Y)$ of the canonical class). This is a joint work with Sergey Finashin.
12:10 PM – 12:30 PM 119-AB Short Communications

Solving Physics Equations Using Orthosymplectic Reduction Superalgebras

The orthosymplectic Lie superalgebras $\mathfrak{osp}(1|2)$ and $\mathfrak{osp}(2|2)$ are utilized in finding solutions to Dirac's equation and Maxwell's equations, respectively, through the implementation of reduction algebra techniques. Reduction algebras aid in the decomposition of an algebra's irreducible modules as modules over a subalgebra. We see examples and note a larger study of reduction algebras as quantum-type algebras. The talk is a presentation of work with Matthew Dorang and Jonas T. Hartwig.
12:10 PM – 12:30 PM 116-A Short Communications

Stability Analysis and a Second-Order Finite Difference Method for Fourth-Order Neutral Volterra Integro-Differential Equation

This work’s objective is to introduce a numerical method for solving a neutralVolterra integro-differential equation that involves fourth- and second-orderderivatives. First, the stability properties of exact solution are analyzed. To solve thisproblem numerically, on the uniform mesh, the finite difference method, includingthe composite trapezoidal rule for the integral part of the equation, is used. Themethod has been demonstrated to be second-order convergent in the discretemaximum norm. In order to verify the efficiency of the suggested method,numerical examples are given.
12:10 PM – 12:30 PM 120-AB Short Communications

Time-Minimizing Navigation on Riemannian Manifolds in Generalized Wind

In this talk, we present the purely geometric solution to the generalized minimum-time navigation problem by means of Riemann-Finsler geometry, which encompasses as particular cases the classical Matsumoto's slope-of-a-mountain problem under gravity and Zermelo's navigation problem on Riemannian manifolds in the presence of space-dependent wind, among other new scenarios. Having constructed a two-parameter model of a slippery mountain slope characterized by traction coefficients, by the anisotropic deformation of the background Riemannian metric and rigid translation with the use of the rescaled generalized wind, we obtain the new Finsler metrics of general $(\alpha, \beta)$-type. The strong convexity conditions under which the related time-minimizing trajectories can be described as Finslerian geodesics are thoroughly established. Besides the theoretical results referred to geometric properties of the solution, we are concerned with its effective applications to modern theoretical physics and mathematical modelling in low dimensions, where time-minimizing geodesics play the key role. In particular, the new setting has significant physical relevance, as it more accurately models real-world scenarios involving movement under an arbitrary type of wind and slope. Moreover, the evolution of time fronts and the behavior of Finslerian geodesics in relation to various impacts of the generalized wind and direction of motion in the slippery slope model are discussed and illustrated by some examples.
12:30 PM – 12:50 PM 116-A Short Communications

An Unconditionally Stable Algorithm for the Time-Fractional BBMB Equation and Convergence Analysis

In this work, we develop an efficient numerical approach to deal with the time-fractional Benjamin-Bona-Mahony-Burger equations. The Benjamin-Bona-Mahony-Burger equation is a significant tool to describe the unidirectional propagation of long waves in specific nonlinear dispersive models. We utilize the Crank-Nicolson method in time with exponential B-splines in space. We establish convergence and stability of the proposed scheme. Due to the unavailability of the exact solution, the double mesh method is used for error estimates. The numerical simulations validate the theory, and a comparison with existing methods displays the efficacy of the proposed technique.
12:30 PM – 12:50 PM 115-C Short Communications

Canonical Parameters on Timelike Surfaces in Pseudo-Euclidean 4-spaces

We introduce special isotropic parameters (which we call canonical parameters) for some classes of timelike surfaces in the Minkowski 4-space and the pseudo-Euclidean 4-space with neutral metric, namely: zero mean curvature surfaces, surfaces with parallel normalized mean curvature vector field, and marginally trapped (quasi-minimal) surfaces. These parameters allow us to describe these classes of surfaces in terms of minimal number of invariant functions satisfying a natural system of partial differential equations. This solves the Lund-Regge problem for timelike surfaces.The author is partially supported by the National Science Fund, Ministry of Education and Science of Bulgaria under contract KP-06-N82/6.
12:30 PM – 12:50 PM 120-AB Short Communications

Enumerating Meanders via Dynnikov Coordinates

In 1912, Henri Poincaré posed the problem of determining the number of distinct simple closed curves intersecting a fixed line at a given number of times. These configurations, later called meanders by Vladimir Arnold in 1987, have been studied by many researchers and remain a compelling subject.In this work, we present an algorithmic approach for the enumeration of meanders via Dynnikov coordinates, which assign integer-valued vectors to isotopy classes of essential simple closed curves on the punctured disk. By encoding the geometric structure of a meander within this coordinate system, our method enables effective computation and facilitates the detection of such curves.
12:30 PM – 12:50 PM 115-A Short Communications

Fixed Point Results in Neutrosophic Fuzzy Banach Spaces

Fixed point results in Neutrosophic Fuzzy Banach spacesRamakant Bhardwaj1,*, Anwesha Ghorai2, Samriddhi Ghosh3, Satyendra Narayan4 1,2,3Department of Mathematics, Amity University Kolkata, Newtown, Kolkata 700135, West Bengal, India4Department of Computer Science and Technology, Algoma University, ON L6V 1A3, Brampton, Canada *Corresponding Author E-mail: rkbhardwaj100@gmail.com,rbhardwaj@kol.amity.edu ABSTRACT The present work introduces the fundamental concept of "Neutrosophic Fuzzy Banach Space". This provides a rigorous framework that extends the classical Banach Space as well as the Fuzzy Banach space by incorporating the notations of truth, indeterminacy, and falsity into the norm structure with respect to classical Neutrosophic Fuzzy sets. Where Fuzzy sets deal with uncertainty using the degree of membership and Neutrosophic set deals with the same using truth, indeterminacy and falsity membership grade. We establish the criteria to establish a Neutrosophic Fuzzy Banach Space and established the behaviour of convergent and Cauchy sequence with this framework. Some fixed point results are established in the said space. Some related examples for fixed point also be formed in the support of established results. Few examples are presented to demonstrate how Neutrosophic Fuzzy Banach Space unify and generalize existing structure while providing a richer environment for analysis. A thorough analysis proposing the fundamental properties as well as the potential utility and theoretical importance of the said space has also been provided. The concepts associated with the space hence established are then utilized along with the concept of contraction mappings to check for fixed point results in it. The results hence obtained, are then considered for application in solving initial value and boundary value problems. Keywords: Fuzzy sets; Neutrosophic sets; Neutrosophic fuzzy set; Normed linear space; Banach space; t-norm; t-conorm; Neutrosophic metric space; Neutrosophic Fuzzy Banach Space.MSC: 47H10, 54H25.
12:30 PM – 12:50 PM 118-AB Short Communications

Hilbert Scale-Based Extension of Homeier-Type Iterative Strategies for Nonlinear Ill-Posed Problems

In this study, a sixth-order Homeier-like method for approximating solutions to nonlinear ill-posed equations within the framework of Hilbert scales, specifically involving monotone operators is proposed. The convergence analysis is conducted under weaker assumptions on the first Fréchet derivative of the operator. For selecting the regularization parameter, adaptive strategy introduced by Pereverzev and Schock (2005) is adapted and the derived error estimate is shown to be of optimal order.
12:30 PM – 1:30 PM Breaks

Lunch on Own

12:30 PM – 12:50 PM 119-AB Short Communications

Resurgent Quantum Gauge Theories

Motivated by the needs of hadronic spectroscopy, we develop a resurgent approach to quantum gauge theories. This theory involves analysis of variational equations on manifolds in function spaces. These function spaces are spaces of sections of bundles on complex finite dimensional manifolds of infinite type. The finite dimensional manifolds are rigid, being determined by transcendental number fields inherent to the theory. The manifolds in question generalize curves of continuum genus and are tightly related to questions in holomorphic dynamics associated with classical and first quantized versions of the theory. The finite dimensional manifolds of infinite type are complexifications of spacetime and its configuration spaces, and encode dynamical singularities that arise in interacting quantum gauge fields in the course of dynamics intrinsic to bound states. We interpret quantum fields as functional pseudodifferential operators. The theory naturally includes theory of functional analogies of vector bundles on functional manifolds. This connection brings about a range of questions about submanifolds of classical function spaces such as the space of diffeomorphisms of various regularity and spaces of Riemannian metrics. Topological toy models of the theory point to functional versions of the theory of characteristic classes and to intersection theory on function manifolds. Holomorphic aspects of the theory are tightly related to certain questions in holomorphic dynamics, in particular, to resurgence theory. One of the results of our analysis is the formulation of a variational principle for functional bundles, that gives us consistent equations for bound states. Solutions to these equations are highly symmetric, in particular they are factorizable according to a functional version of an irregular Riemann Hilbert problem. Our results include interpretation of spectral numbers in terms of geometry of certain functional manifolds.
12:30 PM – 12:50 PM 115-B Short Communications

Symmetries of Hypersurfaces

Beginning from the study of Platonic solids in ancient times, a key program in mathematics is to classify objects of various types with the most symmetries. In algebraic geometry, some of the most basic objects to investigate are hypersurfaces, those spaces defined by a single polynomial equation. To capture all their inherent symmetries, we study these hypersurfaces inside complex projective space.In this work, joint with Jennifer Li, we determine exactly which smooth hypersurfaces of complex projective space have the largest symmetry group in every dimension and every degree. We find that the Fermat equation defines the hypersurface with the most symmetries in all but exactly eight cases and describe these exceptions. The exceptional examples have an exceedingly rich geometry and history extending back to the discovery of the first example by Klein in the 1870s. This presentation will illuminate the 150-year mathematical journey that finally led to the full classification.
12:30 PM – 12:50 PM 118-C Short Communications

Weak Chaos and Li-Yorke Chaos in the Weak Topology of Banach Spaces for Strongly Continuous Semigroups of Operators.

In this talk, we introduce and study the concept of weak hypercyclicity for strongly continuous semigroups of operators on Banach spaces. This leads us to introduce the notions of weak chaos and Li-Yorke chaos in the weak topology of Banach spaces for strongly continuous semigroups of operators. We prove several properties of this class of strongly continuous semigroups and provide necessary and sufficient conditions for a $C_0 $ ,semigroup to be Li-Yorke chaotic in the weak topology. Moreover, we explore the connections between this concept and other existing notions in linear dynamics.
12:50 PM – 1:10 PM 120-AB Short Communications

A Relative Version of Weinstein’s Morphism

In 1989, A. Weinstein introduced a morphism \[\mathcal{A} \colon \pi_{1}(\textup{Ham}(M, \omega)) \to \mathbb{R} / \mathcal{P}_{2}(M, \omega),\] defined via the action functional associated to loops of Hamiltonian diffeomorphisms. Here, \( \textup{Ham}(M, \omega) \) denotes the group of Hamiltonian diffeomorphisms of the symplectic manifold \( (M, \omega) \). A holomorphic variant of this morphism was later proposed by P. Seidel , using pseudoholomorphic curve techniques.This construction was extended by the author to higher homotopy groups:\[\mathcal{A} \colon \pi_{2k-1}(\textup{Ham}(M, \omega)) \to \mathbb{R} / \mathcal{P}_{2k}(M, \omega),\]for all \( 1 \leq k \leq n \), where \( \mathcal{P}_{2k}(M, \omega) \) denotes the group of symplectic periods in degree \( 2k \).The goal of this work is to define a relative version of Weinstein’s morphism. Let \( L \subset (M, \omega) \) be a Lagrangian submanifold, and denote by \( \textup{Ham}(M, L) \) the subgroup of Hamiltonian diffeomorphisms that preserve \( L \).In this talk, we introduce the relative Weinstein morphism\[\mathcal{A}^{L} \colon \pi_{2k-1}(\textup{Ham}_0(M, L)) \to \mathbb{R} / \mathcal{P}_{2k}(M, \omega),\]for each \( k \in \{1, \ldots, n\} \). We will present several explicit computations in the case where \( (M, \omega) \) is a symplectic toric manifold and \( L \subset M \) is a Lagrangian torus fiber.
12:50 PM – 1:10 PM 118-AB Short Communications

Algebraic and C*-Algebraic Invariants for Subshifts

We associate to one-sided subshifts—over finite or infinite alphabets—naturally defined C*-algebras and purely algebraic Leavitt-type algebras that extend the classical graph and Leavitt path algebra frameworks. These constructions retain strong dynamical information: for the subshifts of Ott–Tomforde–Willis, topological conjugacy can be fully characterized through (C*)-algebraic properties, and for countable alphabets equipped with the product metric they also detect isometric conjugacy. Furthermore, algebraic invariants such as K-theory and the socle arise naturally in this setting and provide additional tools for distinguishing subshifts.
12:50 PM – 1:10 PM 115-A Short Communications

Characterizations of Normal 3-Pseudomanifolds with Small Second Face-Number Invariant

In this talk, we characterize normal $3$-pseudomanifolds $K$ with $g_2(K) \leq 4$. It is known that if a normal $3$-pseudomanifold $K$ with $g_2(K) \leq 4$ has no singular vertices, then it is a triangulated $3$-sphere. We first prove that a normal $3$-pseudomanifold $K$ with $g_2(K) \leq 4$ has at most two singular vertices. Subsequently, we show that if $K$ is not a triangulated $3$-sphere, it can be obtained from certain boundary complexes of $4$-simplices by a sequence of operations, including connected sums, edge expansions, and edge folding. Furthermore, we establish that such a $3$-pseudomanifold $K$ is a triangulation of the suspension of $\mathbb{RP}^2$. Additionally, by building upon the results of Walkup, we provide a reframed characterization of normal $3$-pseudomanifolds with no singular vertices for $g_2(K) \leq 9$.
12:50 PM – 1:10 PM 115-B Short Communications

Classifying Torsors of Tori with Brauer Groups

Using Mackey functors, we provide a general theory for classifyingtorsors of algebraic tori in terms of Brauer groups of finite fieldextensions of the base field.This generalizes Blunk's description of the tori associated to del Pezzosurfaces of degree 6 to all retract rational tori, which is essentiallythe largest class where this is possible.
12:50 PM – 1:10 PM 116-A Short Communications

From Bernstein Polynomials to Generalized Bézier Models: Theory, Structure, and Interpretable Imaging Applications

From Bernstein Polynomials to Generalized Bézier Models: Theory, Structure, and Interpretable Imaging ApplicationsFaruk ÖZGERDepartment of Computer Engineering, Iğdır University, 76000-Iğdır, Türkiyefarukozger@gmail.comAytuğ ONANDepartment of Computer Engineering, Izmir Institute of Technology, 35430- Izmir, Türkiyeaytugonan@iyte.edu.trAbstract.This work revisits Bernstein polynomials as the mathematical foundation of Bézier curves and extends their role toward a shape-aware computational framework for medical image analysis. While classical Bézier models are central to geometric design, their fixed polynomial structure limits adaptability in applications that require robustness to noise, controllable deformation, and interpretability—key demands in medical imaging and clinical decision support systems.We introduce analytically grounded generalizations of Bézier curves and surfaces based on extended Bernstein-type blending functions equipped with explicit shape control parameters. These constructions preserve essential geometric properties, including convex hull containment, endpoint interpolation, and numerical stability via De Casteljau–type recursion, while enabling flexible local and global deformation. From a computational perspective, the resulting models admit efficient algorithms suitable for large-scale numerical optimization and inverse problems.The work demonstrates how these generalized Bézier representations naturally integrate into medical image analysis pipelines, particularly for anatomical boundary modeling, contour regularization, and shape-constrained segmentation. Their parametric transparency allows domain knowledge to be encoded directly into the geometric representation, offering an interpretable alternative to purely black-box learning models. Furthermore, connections to Bernstein–Kantorovich operators provide convergence guarantees and robustness properties that are critical when dealing with noisy or low-resolution clinical data.This work positions generalized Bézier modeling as a unifying bridge between computational geometry, numerical analysis, and medical image computing, enabling robust, interpretable, and mathematically principled shape representations for next-generation computer science applications.Keywords. Computational geometry; interpretable shape models; medical imagingMSC 2020. 41A10, 65D17, 68U10
12:50 PM – 1:10 PM 119-AB Short Communications

Hydromagnetic Nanofluids for Improved Thermal Regulation in Engineering Systems

Effective thermal regulation is critical for the reliability, efficiency, and longevity of modern engineering systems. This research investigates the use of hydromagnetic nanofluids, electrically conducting fluids containing suspended nanoparticles, as advanced working media for enhanced heat transfer and thermal control. By incorporating magnetic fields into the flow environment, the study examines how magnetohydrodynamic (MHD) forces influence momentum and energy transport, nanoparticle dynamics, and boundary layer behaviour over a convectively heated stretching /shrinking surface. The governing nonlinear model equations are obtained, analysed, and solved numerically via the shooting technique with the Runge-Kutta-Fehlberg integration scheme. For a shrinking surface, the model exhibits dual solutions, and a linear stability analysis is performed to identify the stable and physically achievable solution. The unique solution is found for the stretching surface case. The effects of emerging thermophysical parameters on the overall flow structure, thermal management, and the inherent irreversibility are quantitatively discussed through graphs and in tabular form. The findings provide practical insights for optimizing thermal management in systems such as heat exchangers, microfluidic devices, electronic cooling platforms, and energy storage technologies, highlighting the potential of MHD nanofluid-based approaches for next-generation engineering applications. Keywords: MHD; Nanofluid; Stretching/shrinking surface; Thermal management; Dual solutions; Stability analysis; Entropy analysis
12:50 PM – 1:10 PM 118-C Short Communications

On Oscillation Theorems of Coles and Kreith

In this talk, we present new oscillation results for linear second-order differential equations that are alternative to the well-known theorems of Coles and Kreith. The canonical and noncanonical cases are discussed in a unified way by using a suitable transformation, the so-called \lq\lq an oscillation-preserving transformation".
12:50 PM – 1:10 PM 115-C Short Communications

On the Existence of a Riemannian Structure for a Given Connection

Let $M$ be a connected and paracompact differentiable manifold of dimension $n \geq 2$, and let $J$ be the vector $1$-form defining the natural tangent structure of the tangent bundle $TM$. An energy function $E: TM \to \mathbb{R}_+$, which vanishes on the null section and is homogeneous of degree two such that the 2-form $\Omega = dd_J E$ has maximal rank (where $d_J = [i_J, d]$ and $d$ is the exterior derivative), defines a metric on the vertical bundle by $g(JX, JY) = \Omega(JX, Y)$ for all $X, Y \in \chi(TM)$ (where $\chi(TM)$ denotes the set of vector fields on $TM$). The relation $i_S dd_J E = -dE$ defines a canonical spray $S$, where $i_S$ denotes the inner product with respect to $S$. The vector $1$-form $\Gamma = [J, S]$ is an almost-product structure ($\Gamma^2 = I$, where $I$ is the identity map), considered by Grifone as a torsion-free linear connection of H. Rund using the Frölicher-Nijenhuis formalism.We demonstrate that the connection $\Gamma$ comes from a Riemannian metric if and only if there exists an energy function $E_0$ satisfying $d_R E_0 = 0$, where $R = \frac{1}{2}[h, h]$ is the Nijenhuis tensor of the horizontal projector $h = \frac{\Gamma + I}{2}$, and such that the scalar 1-form $d_v E_0$ (where $v = \frac{I - \Gamma}{2}$) is completely integrable.Under these conditions, there exists a function $\varphi(x)$, constant on the fibers, such that $e^{\varphi(x)} E_0$ is the energy function associated with the connection $\Gamma$.The equation $d_R E_0 = 0$ reduces to a system of linear equations and is, therefore, explicitly solvable. Once the function $E_0$ is obtained, one must verify that $d_v E_0$ is completely integrable. The function $\varphi(x)$ is then determined by the condition $d_h(e^{\varphi(x)} E_0) = 0$. Several explicit examples illustrate the effectiveness of this method.
1:10 PM – 1:30 PM 115-C Short Communications

A Formula for the $\alpha$-Futaki Character

\'Alvarez-C\'onsul--Garcia-Fernandez--Garc\'ia-Prada introduced the K\"ahler-Yang-Mills equations. They also introduced the $\alpha$-Futaki character, an analog of the Futaki invariant, as an obstruction to the existence of the K\"ahler-Yang-Mills equations. The equations depend on a coupling constant $\alpha$. Solutions of these equations with coupling constant $\alpha>0$ are of utmost importance. We provide a formula for the $\alpha$-Futaki character on certain ample line bundles over toric manifolds. We then show that there are no solutions with $\alpha>0$ on certain ample line bundles over certain toric manifolds and compute the value of $\alpha$ if a solution exists. We also relate our result to the existence result of Keller-Friedman in dimension-two.
1:10 PM – 1:30 PM 118-AB Short Communications

A Functional Identity for the Hilbert Metric

The Hilbert metric is defined as the logarithm of the cross-ratio determined by two points $a,b \in \mathbb{B}^2$ \[\begin{eqnarray*}h_{\mathbb{B}^2}(a, b) = \log \frac{| u- b||a-v |}{|u-a||b-v|} ,\end{eqnarray*}\]where $ u $, $ v $ are the intersection points of the line $L[a,b]$ through $a$ and $b,$ and the unit circle $ \partial \mathbb{B}^2 $ ordered in such a way that $ \left| u - a \right| < \left| u - b \right| $. The visual angle metric defined for $ a, b \in \mathbb{B}^2 $ by\[\begin{eqnarray*}v_{\mathbb{B}^2}(a, b) = \sup \left\lbrace \alpha : \alpha = \measuredangle (a, z, b), z \in \partial \mathbb{B}^2 \right\rbrace .\end{eqnarray*}\]In this work, we establish a functional identity between the Hilbert metric and the visual angle metric in $\mathbb{B}^2$. This identity leads to sharp distortion estimates for quasiregular mappings and analytic functions, now expressed naturally in terms of the Hilbert metric. We further prove that Hilbert circles coincide with Euclidean ellipses. Computer algebra methods, such as the application of Gröbner bases, are employed in the proof. Acknowledgments.Şahsene Altınkaya is supported by the Scientific and Technological Research Council of Türkiye (TUBITAK) according to the research project 1059B192402218.
1:10 PM – 1:30 PM 119-AB Short Communications

Darcy-Forchheimer Hybrid Nanofluids Flow with Quadratic Convection Over a Stretched Tube

The study of well-known Darcian fluidic streams and hybrid nanofluids is an essential need of nowadays researchers inregard to their exceptional heat transfer rates and implementations. The significance of hybrid nanofluids in controllingheat transmission cannot be overemphasized. Therefore, this article scrutinizes the Darcy Forchheimer flow of hybridnanofluid toward a flexible tube. The flow rates near the surface of the cylinder are investigated by applying the DarcyForchheimer theory while examining the heat transfer rate, nonlinear convection expressions are used. The analysis alsoconsiders thermal radiation and chemical reactions. One of sophisticated numerical approach Runge-Kutta method(RK4) is selected for the proposed problem’s solution. The main novelty of present research is to examine the characteristics of hybrid nanofluids in the context of heat transfer over an extending cylinder for the purposes of enhancementregarding thermal transference and inertial impacts. Results shows that hybrid-based nanofluid provides upsurges in solidvolume fraction of nanoparticles accompanied by an enhancement in the heat transfer rate by 4.32%, 5.8%, and 14.46%individually. The outcomes witnessed that hybrid based proposed nanofluids increased thermal transportation processesmore effectively than other nanofluids.
1:10 PM – 1:30 PM 115-B Short Communications

Derivative of the Circulation Invariant and Preservation of the Diffeomorphism of Vortex Filaments

In vortex dynamics of matter, the concept of a kern serves as a fundamental structure for understanding the transport of vortex motion of matter in incompressible spiral flows that create the kern of an elliptical vortex. A vortex kern is defined as the core of a cone where, at the boundaries of the kern, the vortex formation lines act together to form an alternating right and left coherent structure that is preserved under the conditions of "ideal" twisted spiral filaments that behave as autowaves. The study of such complex vortex topological structures ($3R$) is central to understanding both the local and global topology of matter distribution in a closed vortex.In this paper, the differential properties of vortex helicity, a well-known topological invariant governing the quantities μ and the Lie derivative in the three-dimensional case were investigated. Helicity, defined by the volume integral of the scalar product of the velocity and vortex formation fields, remains constant in time in Euler dynamics. The behavior of the helicity functional for infinitesimal deformations of the flow map, considering variations that preserve the diffeomorphic structure of vortex filaments with their own spin and twist was analyzed.I have determined that the derivative $μ$ (“myu”), characterizing the microvortex circulation vector, relative to smooth deformations of the vortex kern boundary can be expressed through boundary flows of helicity density and tangential flow components. The variational formulation emphasizes the invariance of the microvortex vorticity vector relative to volume-preserving diffeomorphisms of vortex filaments passing through the kern, with conservation of the vector and velocity of circulation of matter transfer.In addition, it was found that during a smooth transition to the center of an elliptical vortex, the conservation of helicity implies a limitation on the tangential stretching of the vortex formation lines, which gives an idea of the stability and constancy of such structures. This result links the conformal geometry and vortex dynamics of matter, suggesting that the dynamics of the vortex filaments that make up the kern carcass are regulated by the global vortex potential of the elliptical vortex kern, which determines its energy and stability.Accurate understanding of this vortex mechanism opens the way for the application of models of interaction of closed vortices of different spins in both theoretical hydrodynamics and CFM.
1:10 PM – 1:30 PM 120-AB Short Communications

Extrinsic Geometry of Foliations

\documentclass{article}\title{Extrinsic Geometry of Foliations}\author{\normalsize Vladimir Rovenski \quad ({\small E-mail: {\tt vrovenski@univ.haifa.ac.il}}) \\ {\small Department of Mathematics, University of Haifa, Israel}}\begin{document}\date{}\maketitle\vskip-5mm\centerline{In memory of friend and colleague Professor Pawe\l \ Walczak (1948-2025)}\bigskipExtrinsic geometry of foliations, presented in a monograph by V. Rovenski and P. Walczak, deals with properties of leaves (submanifolds of a Riemannian manifold), which depend on the second fundamental form. The part of the Riemann tensor of a foliation, called the mixed or mutual curvature, depends on the first derivative of metric and belongs to extrinsic geometry. In this talk, I will discuss the concepts and topics of extrinsic geometry of foliations recently introduced by V. Rovenski.1. Weak metric structures, i.e., the complex structure in almost Hermitian, almost contact and $f$-contact manifolds and their subclasses is replaced by a nonsingular skew-symmetric tensor, generalize the classical structures and allow finding new applications. We discuss our latest results on geodesic and Killing fields, Ricci-type solitons and Einstein-type metrics, the $(\kappa,\mu)$-nullity condition, etc. in this new area of Riemannian geometry.2. Mutual curvature invariants of a Riemannian manifold, being an alternative to Chen's $\delta$-invariants, use the mutual sectional curvature of subspaces of the tangent bundle, are well adapted to foliated manifolds and submanifolds and can be applied in the natural sciences. We discuss our recent results on variations of Willmore-type functionals and the corresponding geometrical inequalities, including our curvature invariants and the squared mean curvature, as well as ideal immersions of foliated manifolds.\end{document}
1:10 PM – 1:30 PM 116-A Short Communications

Finite Difference Scheme for Two-Dimensional Poisson Equation with the Multiple Integral Boundary Condition

In this talk, we present a numerical method for solving the two-dimensional Poisson equation on a rectangular domain with a nonlocal boundary condition given by a double integral. The presence of this non-classical boundary condition prevents the use of standard techniques such as separation of variables, making the problem challenging from both analytical and numerical perspectives.We introduce a finite difference approach in which the integral term is approximated using the two-dimensional trapezoidal rule. By reformulating the nonlocal boundary condition in terms of interior grid points and partitioning the computational domain into boundary and interior components, we reduce the original problem to a set of Poisson problems with classical boundary conditions. The solutions of these auxiliary problems are then combined to construct the solution of the original nonlocal problem.This strategy leads to a significant reduction in computational complexity, as it requires solving a linear system of much smaller dimension than that of the full discretization. Under suitable assumptions on the kernel, we establish the validity of the proposed approach and illustrate its effectiveness.
1:10 PM – 1:30 PM 115-A Short Communications

On the Minimal Total Curvature of Cubical Spun 2-knots

We say that a cubical 2-knot $K^{2}$ is an embedding of the 2-sphere in the 2-skeleton of the canonical cubulationof $\mathbb{R}^4$. In this paper, we generalize the notion of minimal lattice curvature of one-dimensional knot type to cubical knots of dimension two, as the infimum over all the total curvatures of cubical 2-knots isotopic to the given knot type. In this talk, we address the following question: What is the minimal total curvature of a knot type if it is a cubical spun 2-knot? For this family of cubical 2-knots, we estimate an upper bound.
1:10 PM – 1:30 PM 118-C Short Communications

Resonance Structure of a Periodically Forced Delay Equation Model of the El Niño Southern Oscillation

The El  Ni$\tilde{\textrm{n}}$o Southern Oscillation (ENSO) is a major climate   phenomenon characterized by sea surface temperature variations in the   Equatorial Pacific Ocean. Conceptual models following the delayed-action   oscillator approach simplify its essential physics to tractable mathematical   models in the form of delay differential equations (DDEs). We perform a detailed bifurcation analysis of an ENSO DDE model introduced in 1988 by Suarez and Schopf, with an additional forcing term that is motivated by   ENSO’s tendency to phase-lock with the seasonal cycle. We show that this   periodically forced nonlinear scalar DDE exhibits a rich resonance structure   of dynamics on invariant tori. Moreover, we demonstrate how chaotic dynamics   emerges when resonance tongues start to overlap as one varies the external   forcing frequency, which is equivalent to varying the strength of the nonlinearity.

1:30 PM – 1:50 PM 115-A Short Communications

Crystallizations of Small Covers Over the n-simplex and the n-prism

A crystallization of a PL manifold is an edge-colored graph that corresponds to a contracted triangulation of the manifold, facilitating the study of its topological and combinatorial properties. A small cover over a simple convex $n$-polytope $P^n$ is a closed $n$-manifold with a locally standard $\mathbb{Z}_2^n$-action such that its orbit space is homeomorphic to $P^n$. In this talk, we will discuss the crystallizations of small covers over the $n$-simplex $\Delta^n$ and the prism $\Delta^{n-1} \times I$. It is known that the small cover over the $n$-simplex $\Delta^n$ is $\mathbb{RP}^n$. For every $n\geq 2$, we prove that $\mathbb{RP}^n$ has a unique $2^n$-vertex crystallization. We also demonstrate that there are exactly $1 + 2^{n-1}$ D-J equivalence classes of small covers over the prism $\Delta^{n-1} \times I$, where $n\geq 3$. For each $\mathbb{Z}_2$-characteristic function of $\Delta^{n-1} \times I$, we present the construction of a $2^{n-1}(n+1)$-vertex crystallization of the small cover $M^n(\lambda)$ with regular genus $1 + 2^{n-4}(n^2 - 2n - 3)$, where $n\geq 4$. The concept of regular genus for closed PL manifolds extends the notions of surface genus and Heegaard genus for 3-manifolds to higher dimensions. Classifying PL $n$-manifolds based on regular genus is a fundamental problem in combinatorial topology. The classification of closed orientable prime PL 4-manifolds up to regular genus 5 is known. As a consequence of our construction, we get four orientable and four non-orientable $\mathbb{RP}^3$-bundles over $\mathbb{S}^1$ up to D-J equivalence with regular genus 6.
1:30 PM – 1:50 PM 118-C Short Communications

Data-Driven Modeling of Dengue Transmission in Indonesia

We present a data-driven approach to modeling dengue transmission using cumulative surveillance data. Starting from a cumulative incidence function, we introduce a generating operator that reconstructs state variables in a compartmental epidemic model. The framework is applied to a host-vector SEIR-SI model, in which time-dependent transmission rates are implicitly inferred from data. Weekly cumulative dengue cases are approximated using a linear combination of logistic functions, allowing explicit expressions for the exposed, infected, recovered, and susceptible populations to be reconstructed from observed data. Based on the reconstructed dynamics, a time-varying effective reproduction number $R_{\mathrm{eff}}(t)$ is derived and analyzed as an indicator of epidemic trends. Numerical simulations using dengue incidence data from Indonesia demonstrate that the proposed method can reproduce observed outbreak patterns. This work highlights the use of cumulative data as a generator for solution reconstruction in compartmental epidemic models and provides a mathematically tractable tool for data-driven epidemic analysis.
1:30 PM – 1:50 PM 120-AB Short Communications

Geometry of Spacelike Hypersurfaces with Statistical Structure in Generalized Robertson-Walker Spacetimes

In this work, we investigate the geometry of generalized Robertson–Walker (GRW) spacetimes by treating their fibers as statistical manifolds, thereby equipping the spacetimes with a statistical structure. A non-trivial example is presented to illustrate this construction. We derive the expression for the statistical Ricci tensor of a GRW spacetime endowed with such a structure and examine its statistical spacelike hypersurfaces. In this context, we establish necessary and sufficient conditions for the existence of a statistical Ricci soliton on these hypersurfaces. Further, we analyze the case where the fiber itself admits a statistical Ricci soliton and obtain the conditions under which the corresponding GRW spacetime admits an almost Ricci soliton structure. Finally, we consider the situation in which both the fiber and the ambient GRW spacetime are Ricci solitons, and we determine the condition under which the corresponding statistical spacelike hypersurfaces also admit a Ricci soliton structure.
1:30 PM – 1:50 PM 115-C Short Communications

Killing Tensors on Symmetric Spaces

I will present new results on geometry and algebra of higher rank Killing tensor fields on Riemannian symmetric space, with a particular focus on the following question: Is any Killing tensor field on a symmetric space a polynomial in Killing vector fields? The talk will include some joint results with Vladimir Matveev (Germany) and Owen Dearricott and An Ky Nguyen (Australia).
1:30 PM – 1:50 PM 116-A Short Communications

M-Matrices and Discrete Problems with Nonlocal Boundary Conditions

The talk is based on some recent joint results obtained with Vytautas Būda (ISM University of Management and Economics, Vilnius), Mifodijus Sapagovas (Vilnius University) and Olga Štikonienė (Vilnius University). We present a finite difference method for the Poisson equation with nonlocal boundary conditions, and consider the case where the matrix of the resulting system of linear equations is an $M$-matrix. Necessary and sufficient conditions for the problem to be described by an $M$-matrix are formulated using the parameters of the nonlocal boundary conditions. The proof is based on the explicit form of the inverse matrix for the classical case. We consider examples of one-dimensional and two-dimensional problems. Another approach is to explore the spectrum of such problems. This also allows us to find the values of the nonlocality parameters for which a finite difference scheme is described by an $M$-matrix. However, for problems with nonlocal conditions, the dependence of the spectrum on the nonlocality parameters can be very complicated. In the two-dimensional case, this is easier to investigate if we can separate the variables, but not all nonlocal conditions allow this.
1:30 PM – 1:50 PM 119-AB Short Communications

Modeling the Impact of Hyperthermia on Tumor Growth and Glucose Diffusion in Biological Tissues

This study develops a mathematical model to analyze heat and mass transfer in tumor-affected biological tissues during local hyperthermia therapy. The model focuses on thermogenesis, thermolysis, ATP dynamics, and heat homeostasis to quantify the effects of controlled heating on tumor metabolism and glucose diffusion. Using Pennes’ Bioheat equation, temperature variations in finite tissue containing a tumor are estimated, while a modified tumor growth equation incorporating thermal damage simulates tumor progression. The finite difference method and Euler’s method are applied to solve the equations under hyperthermia conditions ranging from 39°C to 43°C. The model is validated by comparing simulated tumor and glucose concentration profiles with existing studies. Results demonstrate that higher temperatures significantly reduce tumor proliferation by increasing thermal damage and decreasing glucose availability, ultimately leading to tumor shrinkage. This research highlights the critical role of temperature regulation in tumor treatment and provides a computational tool for optimizing hyperthermia-based cancer therapies.
1:30 PM – 1:50 PM 118-AB Short Communications

The Square Roots of Some Classical Operators

We give complete descriptions of the set of square roots of certain classical operators, often providing specific formulas. The classical operators included in this discussion are the square of the unilateral shift, the Volterra operator, certain compressed shifts, the unilateral shift plus its adjoint, the Hilbert matrix, and the Cesaro operator.
1:30 PM – 1:50 PM 115-B Short Communications

Uniform Bounds on S-Integral Preperiodic Points for Chebyshev Polynomials

Let $K$ be a number field with algebraic closure $\bar{K}$, let $S$ be a finite set of places of $K$ containing all the archimedean places of $K$ and let $\alpha, \beta \in \bar{K}$. We say that $\beta$ is $S$-integral relative to $\alpha$ if no conjugate of $\beta$ meets any conjugate of $\alpha$ at primes lying outside of $S$. For a rational map $\varphi: \mathbb{P}^1 \to \mathbb{P}^1$ defined over a field $K$, a point $x\in \mathbb{P}^{1}(\bar{K})$ is preperiodic if there exist distinct positive integers $m, n$ such that $\varphi^m(x) = \varphi^n(x)$. In this talk, we will discuss uniformity results on the number of $S$-integral preperiodic points for a Chebyshev polynomial. In particular, suppose that $\varphi:\mathbb{P}^1\to \mathbb{P}^1$ is a Chebyshev polynomial and $\beta \in K^{\times}$ is not a preperiodic point of $\varphi$, i.e., $\beta$ is not of the form $\zeta +\zeta^{-1}$ for any root of unity $\zeta$. Then we will see that there exists a constant $C:=C([K:\mathbb{Q}],S)$ such that for any such $\beta$, if $\alpha$ is preperiodic and $S$-integral relative to $\beta$ then the size of $\mbox{Gal}(\bar{K}/K)$-orbit of $\alpha$ is bounded by the constant $C$.
2:00 PM – 3:30 PM Benjamin Franklin Stage Films @ ICM

3Blue1Brown

Film: 3Blue1Brown (3b1b) is primarily a YouTube channel focused on explaining math visually.

Some lessons cover foundational topics, especially those a STEM undergraduate would need to learn. Others are playful explorations of puzzles and beautiful problems. In all cases, the goal is to make more people love math, whether for its utility or its beauty, following a philosophy that any such love begins with deep understanding.

Source: 3blue1Brown

3:00 PM – 3:45 PM 118-AB Section Lecture

At the Intersection of Numerical Analysis and Spectral Geometry

Eigenvalue approximation is a central challenge in numerical analysis, and over the years a multitude of methods - for discretizing the operator and for the resultant discrete system - have been developed and their stability and convergence properties have been analysed. High-accuracy and provably convergent discretization approaches can be used to examine the interplay between the spectrum of an operator and the geometric properties of the domain it is defined on. While computations have been used to guide conjectures in spectral geometry, in recent years approximation-theoretic tools and validated computations are also being used as part of formal proof strategies in spectral geometry. We revisit the process of eigenvalue approximation, from the perspective of computational spectral geometry. Given a particular spectral feature of interest, should we discretize the original problem, or seek a reformulation? Of the many possible approximation strategies, which should we choose? These choices are inextricably linked to the objective: rapid, specialized methods are often ideal for conjecture formulation (prioritizing efficiency and accuracy), whereas schemes with guaranteed error bounds are needed when computation is incorporated into a formal proof strategy. We also explore instances where how the demanding requirements of spectral geometry—specifically the need for rigorous error control or the robust calculation of higher eigenvalues motivate new developments in numerical analysis and scientific computing.
3:00 PM – 3:45 PM 119-AB Section Lecture

Classifying Dynamical Systems with Symmetries

Even though in everyday life it seems completely reasonable that having close relations with a group of people determines to a large extent the development of an individual,  in mathematics it is somewhat surprising when a dynamical system can be completely determined by its group-theoretic relations with other dynamical systems.

We will discuss this rigidity phenomenon in several settings and present recent results, for example demonstrating rigidity for partially hyperbolic dynamical systems in higher-rank semisimple Lie groups of smooth diffeomorphisms of compact manifolds. The motor behind rigidity is the existence of symmetries, that is, commutation relations between dynamical systems. We will explain some of the key mechanisms arising from the interplay of symmetries, that lead to the smooth classification of the dynamics, meaning that up to a smooth change of coordinates, the dynamics is defined via algebraic transformations.  

3:00 PM – 3:45 PM 116-A Section Lecture

Computational Thresholds in High-Dimensional Statistics: The Case of Graph Alignment

Graph alignment is an instance of the NP-hard quadratic assignment problem. It consists, given the adjacency matrices A1, A2 in Rn×n of two graphs, in finding a permutation matrix Π that minimizes the Frobenius norm ∥ΠA1 −A2Π∥F . In this talk we consider the problem from the perspective of high-dimensional statistics: we aim to estimate an unknown permutation π∗ in the symmetric group Sn from the observation of two correlated random adjacency matrices A1, A2. 

We establish the following computational thresholds. We first consider the case where A1, A2 are the adjacency matrices of two correlated Erd\H{o}s-Rényi random graphs G(n, p) in the sparse regime with average degree λ := np = O(1) and edge correlation parameter s ∈ (0, 1). We identify a critical threshold s∗ (λ) for s above which a message-passing, local algorithm succeeds at alignment –that is, recovers a fraction Ω(1) of the entries of π∗, and below which no local algorithm succeeds. This result crucially depends on an associated model of correlated random trees. 

We then consider the case where A1, A2 are two correlated Gaussian Wigner matrices with correlation parameter expressed as s = 1/ √ 1 + σ2 where σ is the “noise” parameter. In this setting we consider a fast spectral algorithm based on the leading eigenvectors of the matrices A1, A2, and identify the critical scaling for noise parameter σ at which the fraction of entries of π∗ correctly recovered goes from 1 − o(1) to o(1). We next consider the convex relaxation approach which obtains the doubly stochastic matrix X that minimizes ∥XA1 − A2X∥F . We obtain upper and lower bounds on the critical noise parameter σ at which a simple postprocessing of X correctly recovers a fraction 1 − o(1) of entries of π∗ . 

We finally identify promising future directions on i) computational thresholds for spectral methods and convex relaxation methods of practical interest, and ii) impossibility results for broad classes of algorithms, notably low degree polynomial algorithms and local search algorithms.

3:00 PM – 3:45 PM 122-AB Section Lecture

Explicit p-Adic Methods for Rational Points

We survey explicit p-adic methods for determining sets of rational points on curves of genus 2 or more, after the work of Chabauty. This starts with the work of Coleman in 1985, which was then reframed by Kim's foundational work on Selmer varieties, and made explicit in certain cases by Balakrishnan, Besser, Dogra, Muller, Tuitman, and Vonk over the last decade. We highlight notable curves where these methods have succeeded and discuss related recent work.
3:00 PM – 3:45 PM 115-B Section Lecture

From the Cherlin-Zilber Conjecture via Sharply 2-Transitive Groups to the Burnside Problem

We review the current state of the Cherlin-Zilber Algebraicity Conjecture on simple groups of finite Morley rank, which states that every such group is the group of K-rational points of an algebraic group for some algebraically closed field K. We will explain the relevance of sharply 2-transitive groups as a potential source of counterexamples and how the Burnside problem necessarily comes into the picture.
3:00 PM – 4:30 PM 117-A IMU Panel

IMU Panel: Committee on Publishing

Lynn Heller

Beijing Institute of Mathematical Sciences and Applications

Fraudulent Publishing in Mathematical Sciences

Publishing is central to our work as scientists: it communicates results, establishes priority, and forms the basis for recognition and evaluation. In recent years, however, fraudulent publishing has become a serious problem, through predatory journals, citation manipulation, paper mills, and fake editorial practices. This talk will discuss how these developments affect the mathematical sciences and present the recent IMU/ICIAM recommendations. It will emphasize what mathematicians can do: choose journals responsibly, refuse to support dubious venues, resist the misuse of metrics, mentor younger colleagues, and insist that research evaluation be based on quality, integrity, and expert judgment.

Jim Portegies

Eindhoven University of Technology

The Leiden Declaration on Artificial Intelligence and Mathematics

Recent advances in AI technologies threaten important values held in our community. Rooted in a joint conviction that as mathematicians, we have a responsibility to ensure the continued flourishing of our discipline, following a conference on Mechanization and Mathematical Research at the Lorentz Center at Leiden University, 17 authors began drafting recommendations on the future relations between the mathematical community and the new technology. I will explain how the resulting Leiden Declaration on Artificial Intelligence and Mathematics developed and share our perspective on the steps ahead for the community.

Q & A

Mark Wilson, Q & A Chair, Smith College

Jarod Alper, University of Washington

Michael Harris, Institut de Mathématiques de Jussieu

Bryna Kra, Northwestern University 

Moritz Schubotz, Leibniz Institute for Information Infrastructure 

 

3:00 PM – 3:45 PM 115-A Section Lecture

The Classification of 3-Fold Flops

This talk will overview recent progress in understanding and classifying one of the most elementary of birational surgeries within algebraic geometry, namely 3-fold flops, through the development of a noncommutative version of singularity theory.
3:00 PM – 3:45 PM 118-C Section Lecture

The Impact of Schur Multipliers in Harmonic Analysis and Operator Algebras

Schur multipliers are basic linear maps on matrix algebras. Their close (albeit still intriguing) connection with Fourier multipliers establishes a solid bridge between harmonic analysis and operator algebras. I will survey the growing impact of Schur multipliers over the past 15 years, with particular attention to recent bounds on Schatten p-classes. I will also present applications in harmonic analysis on group von Neumann algebras and operator rigidity phenomena for higher-rank Lie groups and lattices. Key novelties arise from new insights into nonToeplitz Schur multipliers and unprecedented connections with highly singular operators from Euclidean harmonic analysis.
3:00 PM – 3:45 PM 120-AB Section Lecture

Universality for Two Dimensional Kinetically Constrained Spin Models

Kinetically constrained models (KCMs) are interacting particle systems introduced in the '80s by condensed matter physicists. These models provide accessible stochastic systems with glassy-type dynamics. The key mechanism behind their complex evolution is dynamical facilitation, embedded via appropriate kinetic constraints. KCMs are tightly related to bootstrap percolation, a widely studied monotone cellular automaton. Recently, KCMs have inspired the construction of quantum spin chains to explore many-body localization in the absence of disorder. I will begin with a short review of KCMs' main features and the behavior of two popular models. Then, I will focus on the KCMs counterpart of the famous “universality problem” for two-dimensional bootstrap percolation. In particular, I will highlight the major new features that emerge for KCMs with respect to bootstrap percolation.
3:00 PM – 3:45 PM 121-AB Section Lecture

Volume Functions and Boundary Data of 3-Dimensional Hyperbolic Manifolds

We review recent progress on two closely related sets of questions concerning convex co-compact hyperbolic manifolds, or convex domains in those manifolds, such as their convex core. The first set of questions is to what extent the hyperbolic metric on such a manifold is uniquely determined by either of two possible geometric data on their boundary. The second aspect is the ``volume'' associated to such a manifold, such as the renormalized volume of a convex co-compact hyperbolic manifolds. The relation between the two is provided by the first variation of the volume, which involves the two kinds of boundary data as ``conjugate'' variables. While progress has recently been made on some questions, other remain open. New connections have recently emerged, with physics (and in particular the AdS/CFT correspondence) as well as with probability theory (the Loewner energy).
3:30 PM – 4:30 PM Terrace Ballroom Public Lecture

AI and Humanity's Long Conversation

Mathematics has been called humanity's long conversation. Observations of Euclid, Pythagoras, Euler and Poincaré still occupy the minds of mathematicians today. This conversation has experienced shocks and challenges, including the crisis of foundations in the early 20th century, and the first computer assisted proofs in the second half of the 20th century. We are currently in the midst of another shock, with the rise of formal proof and the first signs of AI systems helping to produce research-level mathematics. This raises questions of fundamental importance: How should mathematicians respond to AI? Will AI systems help (or hinder) our understanding of the mathematical world? Williamson will discuss some recent developments at the interface of mathematics and AI, with the aim of having a clearer picture of this unique point in the history of mathematics.

4:00 PM – 4:45 PM 118-C Section Lecture

A Fourier Extremal Problem

We provide an overview of some recent results concerning an extremal problem in Fourier analysis. We focus on the determination of the norm of the point evaluation functional at the origin in the Paley--Wiener spaces and the characterization of the associated extremal functions. We will discuss the properties of the zeros of these extremal functions and the asymptotic behavior of the norms.A particularly interesting case is when p=1, where the extremal function, the Hörmander-Bernhardsson function, has extraordinarily rich properties and different characterizations that allow its computation.We will concentrate on the results obtained in collaboration with O. Brevig, A. Chirre, K. Seip, and more recently in collaboration with A. Bondarenko, D. Radchenko and K. Seip.
4:00 PM – 4:45 PM 115-C Section Lecture

Counting on the Past: The Birth of Combinatorics in Classical India

Long before combinatorics was recognized as a formal branch of mathematics, its principles were alive and flourishing in the cultural and intellectual life of the Indian subcontinent. Rooted in the systematic study of Sanskrit prosody (chandas), combinatorial procedures and techniques first emerged around 200 BCE in the Chandaḥsūtra of the Sanskrit prosodist Piṅgala. From these foundations, rules governing combinations and permutations gradually found expression in music and dramatic arts, visual art and architecture, medicine and pharmacology, and even divinatory practices. Yet their assimilation into more specialised mathematical spheres unfolded over a much longer period.The earliest evidence we have for the uptake of combinatorial rules in the mathematical sciences is a short chapter tucked away towards the end of a long and technical work on mathematical astronomy, the seventh century Brāhmasphuṭasiddhānta of Brahmagupta. Its inclusion appears somewhat eclectic relative to the work's primary purpose, and its highly terse nature has meant much of its technical content remained obscure to later authors. Despite this, the chapter caught the notice of the eleventh-century Persian polymath al-Bīrūnī whose exposition remained a key source of insight into the text until very recently. We investigate why this chapter has eluded scholars for so long and how, with the discovery of new source material, we are now in a better position to shed light on its mathematical content.
4:00 PM – 4:45 PM 120-AB Section Lecture

Entropies in Quantum Field Theory

We describe some rigorous results about entropies in Quantum Field Theory that have been obtained in recent years,  with particular emphasize on the results about singular limits of relative entropies. These results are motivated in part  by recent physicists work which however depends on heuristic arguments that  are hard to justify mathematically.  Our main technical tools are from the theory of operator algebras including modular theory and theory of subfactors.

4:00 PM – 4:45 PM 115-B Section Lecture

From Cell Decomposition to Motivic Integration, Hensel Minimality, and Point Counting

Following Macintyre's quantifier elimination result for semi-algebraic p-adic sets from 1976, Denef's cell decomposition from 1984 has played a catalyzing role for both motivic integration and Hensel minimality. Motivic integration has in turn been applied in the Langlands program via transfer principles to change the characteristic of the local field, e.g. for the fundamental lemma. Hensel minimality has been used to study rational points on definable sets, providing non-archimedean analogues of results by Pila-Wilkie in o-minimal structures. I will present some of these results and some open questions.
4:00 PM – 5:00 PM Benjamin Franklin Stage Art & Music @ ICM

From Classroom to Canvas: Creating the ICM Mural with Oluwafemi

Mural Arts Philadelphia has partnered with the Outreach Committee of the International Conress of Mathematicians (ICM) to create an indoor mural which is displayed at the 2026 ICM convening at the Pennsylvania Convention Center. This mural has engaged local students of the Mural Arts Foundations & Innovation program as well as local artist Oluwafemi as he directed them during the 2025 - 2026 school year to fabricate this piece.

The process has explored the intersections of art and mathematics through patterned tessellations and vibrant imagery that highlight the impact of mathematical research—career opportunities, groundbreaking discoveries, and the tools that shape innovation.

Hear from the artist Oluwafemi during his talk on how the process unfolded as well as view a behind the scenes documentary capturing the makings of the mural.

This talk and view of the documentary will take place on the Benjamin Frankling Stage located within Hall E.

4:00 PM – 4:45 PM 122-AB Section Lecture

How many rational points can a curve have?

I will give an overwiew of results and open problems related to the number of rational points on "nice" algebraic curves of genus at least 2 over the rational numbers (or, more generally, over algebraic number fields).

4:00 PM – 4:45 PM 116-A Section Lecture

On Spectral Learning for Odeco Tensors: Perturbation, Initialization, and Algorithms

We study spectral learning for orthogonally decomposable (odeco) tensors, emphasizing the interplay between statistical limits, optimization geometry, and initialization. Unlike matrices, recovery for odeco tensors does not hinge on eigengaps, yielding improved robustness under noise. While iterative methods such as tensor power iterations can be statistically efficient, initialization emerges as the main computational bottleneck. We investigate perturbation bounds, non-convex optimization analysis, and initialization strategies, clarifying when efficient algorithms attain statistical limits and when fundamental barriers remain.
4:00 PM – 4:45 PM 119-AB Section Lecture

On the MLC Conjecture and the Renormalization Theory in Complex Dynamics

The MLC Conjecture (the Mandelbrot set is Locally Connected) describes how quadratic polynomials depend topologically on a parameter. The Conjecture has many geometric and probabilistic counterparts; all of them are the subject of the Renormalization Theory, which analyzes first-return maps to small neighborhoods of special points. In this talk, we outline the current state of this theory, with particular emphasis on the (near-) zero-entropy or Molecule (satellite and neutral) regimes.

4:00 PM – 4:45 PM 118-AB Special Joint Section Lecture

Optimal and Diffusion Transports in Machine Learning

Several problems in machine learning are naturally expressed as the design and analysis of time-evolving probability distributions. This includes sampling via diffusion methods, optimizing the weights of neural networks, and analyzing the evolution of token distributions across layers of large language models. While the targeted applications differ (samples, weights, tokens), their mathematical descriptions share a common structure. A key idea is to switch from the Eulerian representation of densities to their Lagrangian counterpart, through vector fields that advect particles. This dual view introduces challenges, notably the non-uniqueness of Lagrangian vector fields, but also opportunities to craft density evolutions and flows with favorable properties in terms of regularity, stability, and computational tractability. This survey presents an overview of these methods, with an emphasis on two complementary approaches: diffusion methods, which rely on stochastic interpolation processes and underpin modern generative AI, and optimal transport, which defines interpolation by minimizing displacement cost. We illustrate how both approaches appear in applications ranging from sampling and neural network optimization to modeling the dynamics of transformers in large language models.

4:00 PM – 5:00 PM Hall E - Expo Poster Presentations

Poster Presentation by Author - Part 1

"The Negative Order Modified Korteweg-de Vries Equation with a Self-Consistent Source" by Shoira Atanazarova (10 - Partial Differential Equations)

"Determining Wavenumbers for Hall and Electron Magnetohydrodynamics" by Hassan Babaei (10 - Partial Differential Equations)

"Existence and Uniqueness of Solutions for Loaded Mixed-Type Equation with Fractional Integral Operators" by Yulduz Babajanova (10 - Partial Differential Equations)

"Integration of the Negative Rrder Nonlinear Schr\"odinger Equation with Self-Consistent Source" by Iroda Baltaeva (10 - Partial Differential Equations)

"Uniform Inviscid Damping and Vorticity Depletion Near Non-Monotonic Shear Flows" by Shan Chen (10 - Partial Differential Equations)

"On Local Well-Posedness of the Stochastic Incompressible Density-Dependent Euler Equations" by Claudia Lorena Duarte Espitia (10 - Partial Differential Equations)

"Cauchy Problem for Generalized Euler--Poisson--Darboux Equation with Loaded Term" by Zebo Egamberganova (10 - Partial Differential Equations)

"A Constructible Conductivity Cloak via Homogenisation" by Eleanor Gemida (10 - Partial Differential Equations)

"On an Algorithm for Finding Solutions of Initial–Boundary Value Problem for Functional–Hyperbolic Equation with Distributed Parameters" by Narkesh Iskakova (10 - Partial Differential Equations)

"A Topological Derivative-Based Method to Image Inhomogeneities in an Acoustic Waveguide" by Umid Karimov (10 - Partial Differential Equations)

"A Boundary Value Problem for a Degenerate Elliptic Equation with Singular Coefficients" by Kalligul Kazakbaeva (10 - Partial Differential Equations)

"Geometric Rigidity and Unstable Set Decomposition of Normally Hyperbolic Frozen Waves" by Jihoon Lee (10 - Partial Differential Equations)

"A coupled PDE–ODE system with boundary interaction arising in heat transfer" by Le Duc Nhien (10 - Partial Differential Equations)

"Global Boundedness and Pattern Formation in a Flux-Limited Keller–Segel System with Logistic Growth" by Ruiliang Li (10 - Partial Differential Equations)

"Regime Dependent Infection Propagation Fronts in an SIS Model." by Vahagn Manukian (10 - Partial Differential Equations)

"A Nash Stratification Inequality and Global Regularity for a Chemotaxis-Fluid System on General 2D Domains" by Naji Sarsam (10 - Partial Differential Equations)

"Fractional Sturm–Liouville Problem on Metric Graphs" by Ariukhan Turemuratova (10 - Partial Differential Equations)

"Inverse Problems for Nonlinear Parabolic Equations in Degenerate Domains" by Madi Yergaliyev (10 - Partial Differential Equations)

"Non-Local Problems for the Fractional Order Diffusion Equation and the Degenerate Hyperbolic Equation" by Nargiza Yuldasheva (10 - Partial Differential Equations)

"Discrete Wave Turbulence of a Coupled System of Quintic Schrödinger Equations" by Shayan Zahedi (10 - Partial Differential Equations)

4:00 PM – 5:00 PM Hall E - Expo Poster Presentations

Poster Presentation by Author - Part 2

"Nonlocal Ordered Mean Curvature with Integrable Kernel" by Animesh Biswas (8 - Analysis)

"On I-Convergence, I-Limit Point and I-Cluster Point of Sequences of Bi-Complex Numbers" by Shyamal Debnath (8 - Analysis)

"On Nonsmooth Global Implicit Function Theorems for Locally Lipschitz Functions from Banach Spaces to Euclidean Spaces" by Guy Degla (8 - Analysis)

"Structure of Projections in algebras generated by n-potent operators" by Priyadarshi Dey (8 - Analysis)

"On the Injectivity of the Spherical Mean value operator" by SAJITH GOVINDAN KUTTY MENON (8 - Analysis)

"Fractional Maps of Generalized Beta Functions and Their Applications to Astrophysical Reaction Rates" by Hussaini Joshua (8 - Analysis)

"Directional Poincaré inequality on compact Lie groups" by Andre Kowacs (8 - Analysis)

"Counterexamples to the Berger–Coburn and Bauer–Coburn–Isralowitz conjectures for Toeplitz operators on Fock space" by Sam Looi (8 - Analysis)

"Perturbation Ideals and Fredholm Theory in Banach Algebras" by Tshikhudo Lukoto (8 - Analysis)

"A Story-Based Introduction to Time Scale Calculus" by Shekhar Singh Negi (8 - Analysis)

"Pseudodifferential Operators on Noncommutative Tori" by Carolina Neira Jimenez (8 - Analysis)

"Some fixed point theorems in strictly convex Menger PM-spaces" by Rale Nikolic (8 - Analysis)

"Directional Maximal Operators and Kakeya-Type Sets" by Blanca Radillo-Murguia (8 - Analysis)

"STABLE CLOSE-TO-CONVEXITY AND RADIUS OF FULL CONVEXITY FOR SENSE-PRESERVING HARMONIC MAPPINGS" by Ankur Raj (8 - Analysis)

"Proportional Calculus and Proportional Differential Equations: Theory and Applications" by Mayuree Sompui (8 - Analysis)

"Spectral Rigidity of Commutators: Dynamical Stability vs Nilpotency" by Hranislav Stanković (8 - Analysis)

"Oblique Dual Frame Completion in Euclidean Spaces: A Product Matrix Approach" by Gino Angelo Velasco (8 - Analysis)

"Construction of Mercedes-Benz Frames via QR Factorization" by Long Wang (8 - Analysis)

"Restriction and Kakeya maximal estimates in Four Dimensions" by Yufei Zhan (8 - Analysis)

"Weighted estimates for some class of quasilinear operators" by Nazerke Zhangabergenova (8 - Analysis)

4:00 PM – 4:45 PM 121-AB Special Joint Section Lecture

Spectral Gap on Large Hyperbolic Surfaces

4:00 PM – 4:45 PM 115-A Section Lecture

The Commutative Algebra of Congruence Ideals and Applications to Number Theory

Congruences in various forms (between integers, functions, ideals..) play an important role in various parts of mathematics. The starting point of this talk is the notion of congruences between modular forms, and especially algebraic gadgets that capture these congruence, which go by the name of congruence ideals and congruence modules. These play a critical role in Wiles' work on Fermat's Last Theorem, and appear in particular in a commutative algebra technique he developed, namely a numerical criterion for detecting isomorphisms of rings. In recent work with Chandrashekhar Khare and Jeff Manning, we pick up on Wiles' work and generalize the numerical criterion to higher codimension. A critical ingredient is a notion of congruence module in higher codimension: this has turned out to be a key definition whose utility extends beyond the role it plays in the numerical criterion. My talk will survey some of these developments, focusing on the commutative algebraic aspects. Part of it will be report on ongoing work with Patrick Allen, Fred Diamond, Chandrashekhar Khare, and Jeff Manning. The presentation will be leisurely, with a goal of reaching a wide audience.
5:00 PM – 5:45 PM 121-AB Section Lecture

Algebraic Cohomology of Ring Spectra

Homotopy theory studies generalizations of commutative rings, called ring spectra, in which addition and multiplication are not necessarily strictly associative or commutative.  Instead, addition and multiplication are required to be associative and commutative only up to canonical isomorphism, in the same sense that the set {a,b} is in bijection with, but not equal to, the set {b,a}.  I will describe a program for generalizing cohomological invariants of rings and schemes to invariants of ring spectra and spectral schemes.  Perhaps surprisingly, understanding these cohomological invariants plays an essential role in a modern accounting of the homotopy groups of spheres (as reflected in the disproof of Ravenel's Telescope Conjecture).

5:00 PM – 5:45 PM 118-C Section Lecture

Can Quantum Dynamics Emerge from Classical Chaos?

Abstract Anosov geodesic flows are among the simplest mathematical models of deterministic chaos. We explain how, quite unexpectedly, quantum dynamics emerges from purely classical correlation functions. The underlying mechanism is the discrete Pollicott–Ruelle spectrum of the geodesic flow, revealed through microlocal analysis. This spectrum naturally arranges into vertical bands; when the rightmost band is separated from the rest by a gap, it governs an effective dynamics that mirrors quantum evolution.
5:00 PM – 6:30 PM Michael A. Nutter Theater Films @ ICM

Felix Klein - Insights from the Outside

International Premier

Film Directed by Ekaterina Eremenko

Felix Klein was a leading mathematician who connected mathematics with education and society, aiming to make it more accessible. He has a lasting influence on mathematics through the Erlangen Program, viewing geometry through the lense of symmetry.

The documentary Felix Klein – Insights from the Outside explores Felix Klein’s life and his impact on modern mathematics, as well as influences he has in physics and machine learning.

The film screening and following Q&A will take place in the Michael A. Nutter Theater located inside of the Pennsylvania Convention Center.

  • Panelist: Anna Wienhard,
  • Akshay Venkatesh,
  • Steve Trettel,
  • Richard Canary,
  • Ekaterina Eremenko, Max Planck Institute for Mathematics in the Sciences
5:00 PM – 5:45 PM 115-B Section Lecture

Henselianity and NIP Fields

One of the cornerstones of the classic model theory of fields is the work of Ax, Kochen, and Ershov in the 1960's on henselian valued fields like the field of formal Laurent series C((t)) or the field of p-adic numbers Qp. Many of these henselian valued fields are NIP (i.e., they do Not have the Independence Property). The class of NIP structures also includes the stable structures and o-minimal structures, as well as many other important examples from algebra. Consequently, NIP has been a major focus of research in model theory for the past 20+ years. Recently, evidence has emerged suggesting that almost all NIP fields are henselian valued fields. Anscombe and Jahnke have shown that this conjecture amounts to a complete classification of NIP fields, and the author has verified the conjecture (and classification) in the "finite-dimensional" case. More generally, this research has led to some surprising new results and conjectures about NIP commutative rings and topological fields, as well as some unexpected new examples.
5:00 PM – 5:45 PM 116-A Section Lecture

Lifts of Graphs, Complexes, and Codes

Graph lifts are a basic tool in coding theory and combinatorics. Many modern low-density parity-check (LDPC) codes are designed as large lifts of small base graphs, allowing one to scale block length, dimension, and, in some cases, distance, while still maintaining sparsity and enabling parallel encoding and decoding algorithms. Lifts also underpin many expander constructions, ranging from random 2-lifts to more recent Ramanujan and near-Ramanujan families. I will begin with graph lifts used in practical LDPC design, then turn to their natural high-dimensional generalization called lifted product codes. These codes extend the idea of lifts to finite covers of Cartesian products of graphs and provide a general framework for constructing both classical locally testable codes and quantum LDPC codes. Unfortunately, by themselves, lifts do not guarantee good parameters, and all current constructions rely on coboundary expansion, which is expressed in several equivalent forms and naturally generalizes edge expansion in graphs. I will outline this idea and its application to tensor product codes, yielding a high-dimensional analog of the minimum distance in the recent generalizations of Sipser–Spielman codes.
5:00 PM – 5:45 PM 119-AB

Probabilistic Combinatorics at Exponentially Small Scales

In many applications of the probabilistic method, one looks to study phenomena that occur ``with high probability''. More recently however, in an attempt to understand some of the most fundamental problems in combinatorics, researchers have been diving deeper into these probability spaces and understanding phenomena that occur at much smaller probability scales. Here I will survey a few of these ideas from the perspective of my own work in the area. 

5:00 PM – 5:45 PM 118-AB Section Lecture

Quadratic Terms, Lie Brackets and Local Controllability

We study the small-time local controllability, in the vicinity of an equilibrium, of a nonlinear scalar-input system. A natural strategy consists in proving the controllability of the linearized system at the equilibrium and conclude with a local inversion argument. When this linearized system is not controllable, it is necessary to study the quadratic term. In this article, we link several recent results on this subject. We also propose a unified methodology to prove quadratic obstructions to local controllability, that relies on systematic drift estimates.

For finite-dimensional control systems, quadratic terms only generate obstructions to controllability: they introduce coercive drifts in the dynamics, quantified by negative integer Sobolev norms of the control, linked to Lie brackets.

In infinite dimension, the same obstructions persist, but two new behaviors occur. First, quadratic obstructions can be due to drifts quantified by other norms (for instance fractional Sobolev norms); their geometric interpretation is challenging. Second, and more strikingly, small-time local controllability can sometimes be recovered from the quadratic expansion.

The tools developed for these studies are also used to understand the influence of higher order terms on the small-time local controllability, for single or multi-input systems, and in other research areas.

5:00 PM – 5:45 PM 115-A Section Lecture

Representations and Characters of Quantum Affine Algebras at The Crossroads Between Cluster Categorification and Quantum Integrable Models

In this lecture, we survey a number of recent results and developments regarding the representation theory of infinite-dimensional quantum groups (quantum affine algebras and related algebras), as well as their connections with cluster categorification and quantum integrable models. We will also give new examples and conjectures.
5:00 PM – 5:45 PM 122-AB Section Lecture

Secant Sheaves and Weil Classes on Abelian Varieties

Let K be a CM-field, i.e., a totally complex quadratic extension of a totally real field F. Let X be a g-dimensional abelian variety admitting an algebra embedding of F into the rational endomorphisms of X. Let A be the product of X and Pic^0(X). We construct an embedding e of K into the rational endomorphisms of A associated to a choice of an F-blilinear polarization on X and a totally imaginary element q in K. We get the [K:Q]-dimensional subspace HW(A,e) of Hodge Weil classes in the d-th cohomology of A, where d:=4g/[K:Q]. We detail a strategy for proving the algebraicity of the Weil classes on all deformation of (A,e,h) as a polarized abelian variety of split Weil type, where h is an e(K) compatible polarization. We then specialize to the case F=Q, so that K is an imaginary quadratic number field. We survey how the above strategy was used to prove the algebraicity of the Weil classes on polarized abelian sixfolds of split Weil type. The algebraicity of the Weil classes on all abelian fourfold of Weil type follows. The Hodge conjecture for abelian varieties of dimension at most 5 is known to follow from the latter result.
5:00 PM – 5:45 PM 120-AB Section Lecture

Sparse Graphs and Their Benjamini-Schramm Limits: A Spectral Tour

Sparse graphs with bounded average degree form a rich class of discrete structures where local geometry strongly influences global behavior. The Benjamini–Schramm (BS) convergence offers a natural framework to describe their asymptotic local structure. In this talk, we will highlight some spectral aspects of BS convergence and their applications, with a focus on random Schreier graphs and covering graphs. 

We review some recent progress on the spectral decomposition of the local operators on graphs. We discuss the behavior of extreme eigenvalues and the growing role of strong convergence in distribution, which rules out spectral outliers. We also give a new applications of strong convergence to the typical graph distance between vertices and to quantum ergodicity.

6:00 PM – 6:45 PM 121-AB Section Lecture

Approaches on Exotic 4-Manifolds

We describe several methods used to produce exotic smooth structures on 4-manifolds, with an emphasis on closed, simply connected 4-manifolds with small \(b_2\). We conclude with a description of an exotic smooth structure on \(\mathbb{C}P^2\#5\overline{\mathbb{C}P^2}\), using a combination of techniques.
6:00 PM – 6:45 PM 116-A Section Lecture

Combinatorial Contract Design: Recent Progress and Emerging Frontiers

Contract theory studies how a principal can incentivize agents to exert costly, unobservable effort through performance-based payments. While classical economic models provide elegant characterizations of optimal solutions, modern applications, ranging from online labor markets and healthcare to AI delegation and blockchain protocols, call for an algorithmic perspective. The challenge is no longer only which contracts induce desired behavior, but whether such contracts can be computed efficiently. This viewpoint has given rise to \emph{algorithmic contract design}, paralleling the rise of algorithmic mechanism design two decades ago.This lecture focuses on \emph{combinatorial contracts}, an emerging frontier within algorithmic contract design, where agents may choose among exponentially many combinations of actions, or where multiple agents must work together as a team, and the challenge lies in selecting the right composition. These models capture a wide variety of real-world contracting environments, from hospitals coordinating physicians across treatment protocols to firms hiring teams of engineers for interdependent tasks. We review three combinatorial settings: (i) a single agent choosing multiple actions, (ii) multiple agents with binary actions, and (iii) multiple agents each selecting multiple actions. For each, we highlight structural insights, algorithmic techniques, and complexity barriers. Results include tractable cases such as gross substitutes reward functions, hardness results, and approximation guarantees under value- and demand-oracle access.By charting these advances, the lecture maps the emerging landscape of combinatorial contract design, and highlights fundamental open questions and promising directions for future work.
6:00 PM – 6:45 PM 115-A Section Lecture

Group Schemes and Momentum Maps

This talk will be a survey of some rather old results of mine which recently became relevant in number theory due to the work of Sakellaridis (partially in collaboration with Venkatesh and Ben Zvi). More precisely, let X be a smooth variety acted on by a connected reductive group G. Then there is a smooth commutative group scheme acting on the cotangent bundle of X which simultaneously integrates all invariant collective Hamiltonian flows. This group scheme only depends on a certain root datum depending on X and is defined via a universal property. As an example, the so-called universal centralizer of G appears as a special case when X=G. In the talk we will restrict ourselves to the case of X being spherical because, firstly, this is by far the most interesting case and, secondly, some technical difficulties disappear.
6:00 PM – 6:45 PM 118-C Section Lecture

Long Time Dynamics of Space Periodic Water Waves

This lecture will examine recent breakthrough results in understanding the long-time dynamics of space-periodic water waves, focusing on1. KAM theory: bifurcation of Cantor-like families of quasi-periodic solutions, both standing and traveling. Specifically, this includes quasi-periodic traveling Stokes waves, which are a nonlinear superposition of simpler periodic Stokes waves, moving with non-resonant speeds.2. Birkhoff normal form theory: long-time well-posedness. These long time existence results guarantee stability for all solutions with initial datum sufficiently small and smooth.3. Modulational instability of Stokes waves: unstable Bloch-Floquet waves near periodic Stokes waves. While KAM quasi-periodic solutions are linearly stable under co-periodic space perturbations, they may become unstable under wave disturbances of different periods.Because of their theoretical and practical importance, the water wave equations have been studied extensively for centuries. Major challenges stem from the non-local and quasi-linear nature of the vector field, which, in the pure gravity case, is even a singular perturbation of the linear part. In the last decades, after pioneering local well-posedness theory, global well-posedness breakthrough results were established for waves with sufficiently smooth and localized initial data. In contrast, for periodic initial data, solutions often exhibit oscillatory and recurrent behavior and global well posedness remains an open problem. The nonlinear long-term dynamics is heavily influenced by N-wave resonant interactions, which introduce delicate small divisors phenomena. The Hamiltonian and reversible nature of the water waves vector field play a key role.Our results rely on unconventional approaches to KAM and Birkhoff normal form theories for Hamiltonian quasi-linear PDEs (the introduction of pseudo and para-differential normal forms) and a symplectic Kato perturbation theory for separated eigenvalues of Hamiltonian and reversible operators. These ideas and techniques have been pivotal in other recent advances, opening new perspectives in the field.
6:00 PM – 6:45 PM 118-AB Section Lecture

On Complexity of Deterministic Model Based Derivative Free Optimization Methods

In many applications of mathematical optimization, one may wish to optimize an objective function without access to its derivatives. These situations call for derivative-free optimization (DFO) methods. Among the most successful approaches in practice are model-based trust-region methods, such as those pioneered by M.J.D Powell. While relatively complex to implement, these methods are now available in standard scientific computing platforms, including MATLAB and SciPy. However, theoretical analysis of their computational complexity lags behind practice. In particular, it is important to bound the number of function evaluations required to achieve a desired level of accuracy. In this lecture we will discuss a variety of derivative free optimization methods and their worst case complexity bounds. We will then show how to systematically derive complexity bounds for classical model based trust region methods and their modern variations. We establish, for the first time, that these methods can have the same worst case complexity than any other known DFO method. We will conclude with some of the open problems and future directions in this domain.
6:00 PM – 6:45 PM 115-B Section Lecture

Persistent Homology: Representation-Theoretic Foundations and Applications

Topological data analysis (TDA) is an emerging field in applied mathematics that enables us to characterize the shapes of massive and complex datasets using topological methods. In particular, persistent homology and persistence diagrams have recently found applications across a wide variety of scientific and engineering problems. In this talk, I will survey recent research on persistent homology from the perspective of representation theory. Topics include generalizations using derived categories, interval approximation and generalized persistence diagrams, as well as irreducible decompositions of representation varieties for multi-parameter persistence. I will also discuss applications of TDA in materials science. By employing several new mathematical tools developed around persistent homology, one can explicitly extract geometric and topological features embedded in materials, which play a practically important role in controlling their physical functions.
6:00 PM – 6:45 PM 119-AB Section Lecture

Refined Absorption: A New Proof of The Existence Conjecture and Its Applications to Extremal and Probabilistic Design Theory

We discuss the recently developed method of refined absorption and how it is used to provide a new proof of the Existence Conjecture for combinatorial designs. This method can also be applied to resolve open problems in extremal and probabilistic design theory while providing a unified framework for these problems. Crucially, the main absorption theorem can be used as a ``black-box'' in these applications obviating the need to reprove the absorption step for each different setup.
6:00 PM – 6:45 PM 120-AB Special Section Lecture

Surprises in Percolation on Random Graphs

Percolation is a model for random damage to a network. It is one of the simplest models that displays a phase transition: when the network is severely damaged, it falls apart in many small connected components, while if the damage is light, while if the damage is light, connectivity is hardly affected. We study the location and nature of the phase transition on random graphs. In particular, we focus on the connectivity structure close to, or below, criticality, where components display intricate scaling behaviour such that a typical connected component has a bounded size, while the maximal connected component sizes grow like powers of the network size. We review the recent progress that has been made in two important settings: random graphs whose expected adjacency matrix is close to being rank-1, the most prominent examples being the configuration model and rank-1 inhomogeneous random graphs, and dynamic random graphs, i.e., random graphs that grow with time, such as uniform attachment models. Remarkably, these two settings behave rather differently. In all cases, the inhomogeneity of the underlying random graph on which we perform percolation is of crucial importance. In my presentation, I focus on the surprising behaviour of percolation on random graphs with infinite-variance degrees, and on growing random graphs.[This is joint work with Sayan Banerjee, Shankar Bhamidi, Souvik Dhara, Rajat Hazra, Johan van Leeuwaarden, and Rounak Ray.]
6:00 PM – 6:45 PM 122-AB Section Lecture

Topology of Abelian Fibrations

We discuss the topology of abelian fibrations with a focus on the role played by the decomposition theorem and perverse filtrations. Three directions are considered: the P=W conjecture, the topology of Lagrangian fibrations, and the cohomology of the universal compactified Jacobians.
6:45 PM – 8:15 PM 120-C Receptions & Special Events

University Networking (Invitation Only)

By Invitation only. 

7:30 PM – 10:00 PM Michael A. Nutter Theater Films @ ICM

PHENOMENA

Film Directed by Josef Gatti

PHENOMENA is a psychedelic odyssey into the fabric of the universe, guided by a filmmaker and his immersive practical experiments that blur the lines between art and science to reveal nature’s inner workings. Captured entirely by camera with no visual effects or artifice, the unfolding awe-inspiring hyper-real imagery is elevated by music from legendary Nils Frahm and an ethereal electronic original score by Rival Consoles, transforming curious observation into a hypnotic audio-visual adventure spanning from the subatomic to cosmological scales. Tracing the forces and elements shaping the natural world, PHENOMENA is a kinetic sensory experience, exploring the wonders of the universe and our connection to it.

Monday, July 27, 2026

9:00 AM – 6:00 PM Hall E - Expo Expo and Collaborations

Exhibition & Collaboration

9:00 AM – 10:00 AM Terrace Ballroom Plenary Lecture

Prismatic Stable Homotopy Theory

One of the most powerful approaches to the study of algebraic K-theoryis the use of trace methods: that is, approximations of K-theoryby more computable invariants (such as Hochschild homology). In this talk, I'll describe a (conjectural) extension of this methodology to other cohomological invariants in algebraic geometry.
10:15 AM – 11:15 AM Terrace Ballroom Plenary Lecture

Compactifying Moduli Spaces

Moduli spaces parametrize mathematical objects of various kinds, and they are ubiquitous in algebraic geometry. It is frequently the case that these spaces aren't compact, and the "holes" can be seen to correspond to degenerations of the objects being parametrized . For example, two points in the plane can come together, or a smooth curve can degenerate to a singular one. As such, natural compactifications that reflect the geometry of degenerations are highly desirable and elucidating.

 We give several examples and explain recent work constructing a general class of compactifications by using the cohomology theories internal to the objects being parametrized, via hodge theory. This completes the picture laid out by Griffiths at the 1970 ICM. This is work joint with B.Bakker, S.Filipazzi, and M.Mauri.

10:30 AM – 10:50 AM 119-AB Short Communications

Adjoint Integration of Lie Algebroids

The adjoint integration of a Lie algebroid—when it exists—is its minimal (i.e., smallest) Lie groupoid integration. In this talk, we investigate the conditions for the existence of adjoint integrations and develop systematic methods for their construction. We show that such an integration exists if and only if the source-simply connected integration admits a maximal discrete normal subgroupoid; the adjoint integration is then obtained as the corresponding quotient.A key result is that the category of discrete normal subgroupoids—and, in the Poisson setting, Lagrangian discrete normal subgroupoids—is invariant under (symplectic) Morita equivalence. This invariance offers a conceptual explanation for the naturality of minimality in the integration of Lie algebroids.Following the approach of Garmendia and Villatoro, we construct the holonomy groupoid of a Lie algebroid. These results lay the groundwork for our next goal: defining the $C^*$-algebra of this (possibly non-smooth) holonomy groupoid and developing an associated pseudodifferential calculus, with applications to index theory and noncommutative geometry.This is a joint work with Joel Villatoro.
10:30 AM – 10:50 AM 120-AB Short Communications

Almost Bipartite Non-König-Egerváry Graphs

This abstract emphasizes structural properties of almost bipartite non-König–Egerváry graphs, focusing on the interplay between their unique odd cycle and several fundamental vertex sets.A graph is König–Egerváry if the sum of its independence number and matching number equals its order, while almost bipartite graphs are characterized by containing exactly one odd cycle. We show that for each almost bipartite non-König–Egerváry graph, every maximum matching necessarily saturates the maximum possible number of edges in its unique odd cycle.A set of vertices B is critical in the graph G =(V, E) if|B| - |N(B)| = max{|X| - |N(X)| : X is a subset of V}, where N(X) is the open neighborhood of X.We prove that for an almost bipartite non-König–Egerváry graph, its core (the intersection of all maximum independent sets) coincides with its kernel (the intersection of all critical independent sets), a property previously established for bipartite and unicyclic non-König–Egerváry graphs. In addition, we introduce the notions of corona (the union of all maximum independent sets) and diadem (the union of all critical independent sets).We derive a formula for the number of vertices whose removal transforms an almost bipartite non-König–Egerváry graph G into a König–Egerváry graph, showing that this number equals the difference |corona(G)| - |diadem(G)|. Finally, we show that this number equals the order of the graph G if and only if the graph itself is an odd cycle.These results extend the known structural theory of independent sets from bipartite and unicyclic graphs to a broader class of graphs.
10:30 AM – 10:50 AM 115-B Short Communications

Eilenberg-MacLane Spectra and Connective Complex K-Theory as MU-Thom Spectra

We study how the Eilenberg-MacLane spectra $\mathrm{H}\mathbb{F}_2$ and $\mathrm{H}\mathbb{Z}$ and the connective complex $\mathrm{K}$-theory spectrum $\mathrm{ku}$ arise as $\mathbb{E}_3$-$\mathrm{MU}$-Thom spectra. Consequently we calculate as $\mathbb{E}_2$-rings that $\mathrm{THH}(\mathrm{H}\mathbb{F}_2/\mathrm{MU})\cong \mathrm{H}\mathbb{F}_2[\mathrm{BU}]$, $\mathrm{THH}(\mathrm{H}\mathbb{Z}/\mathrm{MU})\cong \mathrm{H}\mathbb{Z}[\mathrm{BSU}]$, and $\mathrm{THH}(\mathrm{ku}/\mathrm{MU})\cong \mathrm{ku}[\mathrm{BU}\langle 6 \rangle]$.
10:30 AM – 10:50 AM 116-A Short Communications

From Symplectic and Contact Geometry to Urban and Architecture Modelling

This work extends results introduced at the ICM 2018 in Rio-de-Janeiro, focusing on the application of differential geometry to Building Information Modeling (BIM) and computational approaches to architecture. Within the scope of that research, the primary objective was to introduce and give some properties around architectural geometry which is an important generalization of the basic geometry. In particular, we developed new models to analyze and assess environmental impacts over the entire life cycle of a product, modeled within an \(n\)-dimensional closed manifold \(M\). This work builds upon the results presented in the book published by my PhD advisor, Banyaga, together with Hurtubise and Spaeth (2024), where the Twisted Morse Homology Theorem is established and the connection with Lichnerowicz cohomology is made explicit. The Lichnerowicz cohomology \(H_\omega^*(M)\) (i.e. cohomology of the complex of differential forms on a smooth manifold with the de Rham differential operator deformed by a closed 1-form \(\omega\)) was initiated by A. Lichnerowicz. Since its introduction, this cohomology has attracted a lot of interest and its importance comes from the fact that it is well adapted to locally conformal symplectic geometry.The aim of this new contribution is to extend this framework by investigating the structure of Lichnerowicz cohomology to identify new cohomological invariants and develop new models to analyze and assess environmental impacts over the entire life cycle of a product in the \(n\)-dimensional closed manifold \(M\).. As we have shown in our previous research, mathematical models and outcomes developed in the context of research projects in architectural geometry often lack interoperability, primarily because the simulation environments used are closed systems rather than open-source platforms. The question that then arises is how to produce a tool that allows the flow of information between the various simulators based on symplectic and contact geometry that are complementary but not integrated.
10:30 AM – 10:50 AM 115-A Short Communications

Geometry of Conformal Riemannian Maps from Manifolds Admitting a Ricci Soliton

In this work, we investigate the geometry of conformal Riemannian maps between Riemannian manifolds, with particular attention to the interaction between such maps and Ricci soliton structures. We derive a Bochner-type identity and establish the conditions under which such maps are harmonic or totally geodesic. In addition, we investigate horizontally homothetic and totally umbilical conformal Riemannian maps between Riemannian manifolds. The study is then extended to the case where the total manifold admits a Ricci soliton structure, and a non-trivial example is provided to illustrate the construction. Within this framework, we obtain conditions under which the fiber and the target manifold of a conformal Riemannian map admit either a Ricci soliton or an Einstein structure. Moreover, we study harmonicity and biharmonicity in this context and provide necessary conditions for conformal Riemannian maps, defined on total manifolds admitting Ricci solitons, to be harmonic or biharmonic. The results contribute to a deeper understanding of the interplay between Ricci soliton geometry and the theory of conformal Riemannian maps, extending earlier developments on harmonic maps and Riemannian submersions.
10:30 AM – 10:50 AM 118-AB Short Communications

Solvability of a Generalized Tricomi Problem for Fractionally Loaded Mixed-Type Equations

In this talk, I will present recent results on the solvability of a generalized Tricomi problem for mixed parabolic–hyperbolic equations with fractional loading. The problem is formulated with an integral gluing condition along the line of type change, which naturally arises in models involving memory and nonlocal effects.I will first discuss the case of a loaded equation associated with the telegraph operator. By reducing the boundary-value problem to an equivalent system of integral equations, I will establish existence and uniqueness results. I will then indicate how these results extend to a broader class of generalized mixed-type equations depending on small parameters.The results provide a natural extension of classical solvability theory for the Tricomi problem and contribute to the analysis of boundary-value problems for mixed-type equations with fractional and nonlocal terms.
10:30 AM – 10:50 AM 115-C Short Communications

Unramified Pro-P Extensions and the Uniform Fontaine–Mazur Conjecture

The uniform version of Fontaine–Mazur Conjecture predicts that uniform analytic pro-p groups cannot occur as Galois groups of infinite everywhere unramified pro-p extensions of number fields. A key invariant governing the structure of such groups is the relation rank r(G), which is difficult to compute in practice. Motivated by work of N. Boston, we identify families of bi-quadratic extensions that come close to violating the conjecture. In this talk, I present our results on whether the Galois groups associated to these bi-qudratic extensions yield genuine counterexamples, using recent results of Hajir, Maire, and Ramakrishna on the deficiency of the p-class tower to compute r(G). This is a joint work with Christian Maire.
10:30 AM – 10:50 AM 118-C Short Communications

Weak Centrality for Certain Tensor Products of C*-Algebras

A unital $C^\ast$-algebra $A$ is weakly central if two maximal ideals $M$ and $M'$ of $A$ coincide whenever $M\cap Z(A)=M'\cap Z(A)$, where $Z(A)$ is the centre of $A$ (see, R. J. Archbold and I. Gogic, The centre-quotient property and weak centrality for $C$*-algebras, Int. Math. Res. Not., 2 (2022), 1173-1216). The $C^*$-algebras satisfying the Dixmier property (in particular, von Neumann algebras) are some prominent examples of weakly central algebras. In this talk, we shall introduce weak centrality for Banach algebras and discuss some of its properties. We use this to discuss the weak centrality of the tensor product $A\otimes_\alpha B$ (a Banach algebra) in terms of the weak centrality of $A$ and $B$, where $A$ and $B$ are $C^\ast$-algebras, and $\otimes_\alpha$ is either the Haagerup or the Banach space projective tensor product. We also identify the largest weakly central ideal of $A\otimes_\alpha B$ in terms of that of $A$ and $B$. We further study the relationship between weak centrality and centre-quotient property for $A\otimes_\alpha B$. This talk is based on our research article (A. Paliwal and R. Jain, Weak Centrality for certain tensor products of $C^\ast$-algebras, https://arxiv.org/abs/2508.08838v1) and some unpublished work.
10:50 AM – 11:10 AM 118-C Short Communications

Characterization of Generalized Hausdorff Operator on Bergman Spaces

In this talk, at first, we will discuss the basic theorems of Hausdorff operator starting from the work of Xiao, for the class of integrable functions on $\mathbb{R}^{+},$ which was later considered by Stylogiannis for the spaces of analytic functions on the complex plane. After that, we will discuss the recent developments of generalized Hausdorff operator generated by the kernal $\phi$ on the weighted integrable spaces on $\mathbb{R}^{+}$ and Bergman spaces on the upper half of the complex plane. Lastly, we explore the boundedness and compactness of the Hausdorff operator on Bergman space on the upper half of the plane.
10:50 AM – 11:10 AM 120-AB Short Communications

Equivalence of Labeled Graphs and Lattices

In $1973$, Harary and Palmer posed the problem of enumeration of labeled graphs on $n \geq 1$ unisolated vertices and $l \geq 0$ edges. In $1997$, Bender et al.\ obtained a recurrence relation representing the sequence $A054548$(OEIS) of labeled graphs on $n \geq 0$ unisolated vertices containing $q \geq \frac{n}{2}$ edges. In $2020$, Bhavale and Waphare obtained a recurrence relation representing the sequence of fundamental basic blocks on $n \geq 0$ comparable reducible elements, having nullity $l \geq \lfloor \frac{n+1}{2} \rfloor$. In this paper, we prove the equivalence of these two sequences. We also provide an edge labeling for a given vertex labeled finite simple graph.
10:50 AM – 11:10 AM 118-AB Short Communications

Exponential Attractor and Explicit Bound on Its Fractal Dimension for a NLS Type Equation

In this short communication, we study a damped nonlinear Schrödinger equation (NLS) in the presence of a nonlocal term on the real line. Through this study, we introduce a new approach that will allow us to prove the existence of a global exponential attractor characterizing the asymptotic behavior of the solutions and containing much of the relevant information about the flow, to which we can reduce the qualitative study of the system. Furthermore, this approach will also allow us to explicitly determine a bound on its fractal dimension as a function of the parameters involved in the equation.
10:50 AM – 11:10 AM 116-A Short Communications

Gauge Theory and the Bogomolov-Miyaoka-Yau Inequality for Symplectic 4-manifolds

We describe recent progress in our work to prove the conjecture that symplectic 4-manifolds with obey the Bogomolov-Miyaoka-Yau inequality. Our method uses Morse theory on the moduli space of non-Abelian monopoles. The method aims to use the fact that there is at least one non-vanishing Seiberg-Witten invariant to produce a solution to the anti-self-dual Yang-Mills equation on a vector bundle with suitable topology over the symplectic 4-manifold. The talk is based on joint work with Tom Leness and the monographs https://arxiv.org/abs/2010.15789 (to appear in AMS Memoirs) and https://arxiv.org/abs/2206.14710
10:50 AM – 11:10 AM 115-A Short Communications

Product of Commutators with b-generalized Skew Derivations on Lie Ideals

Let $R$ be any prime ring of char $(R)\neq 2,3$, $Q_r$ be the right Martindale ring of quotients of $R$, $C$ be the extended centroid of $R$ and $L$ a non-central Lie ideal of $R$. Let $b \in Q_r$. An additive map $F : R \rightarrow Q_r$ is said to be a $b$-generalized skew derivation of $R$, if there exists a skew derivation $d$ of $R$ associated with an automorphism $\alpha$ such that $$F(xy) = F(x)y + b\alpha(x)d(y)$$ for all $x,y \in R$. If $F$ and $G$ are two non-zero $b$-generalized skew derivations of $R$ such that $$[F(X),X][G(X),X]=0$$ holds for all $X\in L$, then all possible forms of the maps $F$ and $G$ are described. It is proved that one of the following conclusions holds: (i) $F(x)=\lambda x$ for all $x\in R$ and for some $\lambda \in C$;(ii) $G(x)=\mu x$ for all $x\in R$ and for some $\mu \in C$;(iii) $R\subseteq M_2(K)$, the algebra of $2\times2$-matrices over a field $K$.
10:50 AM – 11:10 AM 115-C Short Communications

Reversibility in Special Linear Groups

An element of a group is called reversible if it is conjugate to its inverse, and strongly reversible if it can be expressed as a product of two involutions. These notions arise naturally in several areas of mathematics, and their study forms a historically rich and active area of research. While every reversible element in a general linear group over a field is strongly reversible, this correspondence fails for special linear groups. In this talk, I will introduce the concept of reversibility in groups and present a classification of reversible and strongly reversible elements in the complex and quaternionic special linear groups. This is joint work with Krishnendu Gongopadhyay and Chandan Maity.
10:50 AM – 11:10 AM 119-AB Short Communications

Ruled Surfaces as Self-Similar Solutions to the Harmonic Mean Curvature Flow in Minkowski 3-space

Ruled surfaces having a significant importance in geometry as well as other fields like CAD and architecture, are one of the main-stream topics in research at present. In this paper, we classify the ruled surfaces in Minkowski 3-space that are self-similar solutions to the harmonic mean curvature flow (HMCF) under the translation and homothetic motion. We give the classification of such ruled surfaces in accordance with the causality of their rulings in Minkowski 3-space and proved that there is no non-degenerate ruled surface with pseudo-null ruling which is a homothetic self-similar solution to the HMCF.
10:50 AM – 11:10 AM 115-B Short Communications

Small Dehn Surgery and SU(2)

Kronheimer and Mrowka (2004) demonstrated that for any nontrivial knot \(K\subset S^3\) and a rational slope \(r \in [0,2]\), the Dehn surgery manifold \(S^3_r(K)\) is always \emph{\(SU(2)\) non-abelian}—meaning its fundamental group admits a homomorphism to \(SU(2)\) with non-abelian image. For slopes beyond this interval, subsequent work by Baldwin–Sivek (2023), Baldwin–Li–Sivek–Ye (2024), Farber–Reinoso–Wang (2024), and Li–Ye (2025) has extended the \(SU(2)\) non-abelian property to all rational slopes \(r = p/q \in (2,6)\) where \(p = x^e\) or \(p = 2x^e\) for some prime \(x\) and natural number \(e\). The only exceptions arise for the right-handed trefoil knot at slopes of the form \(6 - 1/n\) with \(n\) a positive integer. These advances rely crucially on recent developments in the framed instanton Floer homology of Dehn surgery manifolds, studied over coefficient fields \(\mathbb{C}\) and \(\mathbb{Z}/2\).
11:10 AM – 11:30 AM 118-AB Short Communications

A Posteriori Error Control and Adaptive Space–Time Discretization for Nonlinear Degenerate Equations

Using a fully space–time variational formulation, we develop a numerical approximation scheme for a class of nonlinear parabolic equations. In this approach, the spatial and temporal discretization are addressed simultaneously, allowing for a flexible mesh in space and time, but leading to large fully discrete systems. Additional challenges are encountered in cases when the diffusion is nonlinear, or even degenerate.The scheme relies on a splitting strategy, in which the nonlinear dependencies are considered as algebraic equations, at the expense of new unknowns. This is applied directly to the space–time formulation, leading to an equivalent system that is more suitable for handling degeneracies. Based on this reformulation, we employ a stabilized iterative linearization scheme and establish its convergence in the space–time setting.A central contribution of this work is the development of guaranteed a posteriori error estimators, based on locally equilibrated flux reconstructions on space–time vertex patches. The resulting estimators are fully computable and provide a clear separation between linearization and discretization errors. This enables a reliable adaptive strategy in which the mesh refinement is activated only when the discretization error dominates. In this way, the global number of unknowns is reduced significantly when compared to non-adaptive schemes. Numerical experiments demonstrate that the proposed adaptive space–time method efficiently concentrates the computational effort in regions exhibiting strong space–time variations, yielding accurate solutions at significantly reduced computational cost.
11:10 AM – 11:30 AM 119-AB Short Communications

Algebraic Versions of $\mathbb{T}^2$ and of $\mathbb{P}^1\times\mathbb{P}^1$ and Hochschild Cohomology

We examine the Hochschild cohomology for triangular algebras that capture some aspects of geometry and topology of the torus and of the quadric surface, and for deformations of these algebras. In particular, this shows that the cup product on the Hochschild cohomology of a triangular algebra does not generally follow the intuition coming from monomial algebras. Our examples also demonstrate that the Hochschild cohomology of a deformation of an algebra may not experience the dimension drop but still have a different cup product structure, and that the Hochschild cohomologies of deformations of two derived equivalent algebras may exhibit noticeably different behaviours.
11:10 AM – 11:30 AM 115-C Short Communications

Basic Properties of the Ranks of Tensors

Tensors are higher-dimensional generalisations of matrices, and likewise the main notion of complexity on matrices - the rank - may be extended to tensors. For a long time the main such extension that was considered was the tensor rank. Throughout the past decade however, new notions have arisen. For instance, the slice rank originated in a reformulation by Tao in 2016 of the underlying tool in the breakthrough papers of Croot-Lev-Pach and Ellenberg-Gijswijt (both published in the Annals of Mathematics) on the cap-set problem. The partition rank was then defined one year later by Naslund in a similar context, and several other ranks have blossomed since then. It has now become clear that there is no single canonical notion of rank on tensors, and that the most useful notion instead depends on the application at hand.

In sharp contrast with the matrix case, the properties of the ranks of tensors are still poorly understood. This is largely due to the lack of tools leading to lower or upper bounds on these ranks. We will present several basic properties of the ranks of tensors, including suitable generalisations of the following two facts: that a rank-$k$ matrix must contain a $k$ by $k$ submatrix, and that a matrix has only one minimal-length decomposition up to a change of basis. As in many situations aimed at generalising a property of the rank of matrices to the ranks of tensors, the naive extension of the original property fails in a major way, yet still admits a rectification which is simultaneously not too complicated to state and in a spirit that is very close to that of the original property from the matrix case.

11:10 AM – 11:30 AM 120-AB Short Communications

Combinatorial Invariants Derived from Codes Over Algebraic Structures

Let $\lambda = (\lambda_1, \dots, \lambda_r)$ be a partition of a positive integer $n$, where each $\lambda_i$ is referred to as a part of $\lambda$. A finite Abelian $p$-group of rank $r$ associated with this partition can be expressed as\[G = \mathbb{Z}/p^{\lambda_1}\mathbb{Z} \oplus \dots \oplus \mathbb{Z}/p^{\lambda_r}\mathbb{Z},\]where $p$ is a prime number.Interestingly, the same partition $\lambda$, when viewed through the action of a permutation group on a simple graph, also encodes a numerical semigroup. From this perspective, we construct a specific lattice-based code $\mathcal{C}_{\lambda}$, which serves as a unifying structure connecting these algebraic and combinatorial objects namely, finite Abelian groups, numerical semigroups, and partitions.A powerful combinatorial tool used in the representation theory of groups and algebras called as \textit{standard Young tableaux} emerges naturally from the structure of $\mathcal{C}_{\lambda}$. While existing constructions of standard Young tableaux associated with numerical semigroups typically rely on the \textit{gaps} of the semigroup, our approach offers a novel and more efficient method. In particular, we derive these tableaux using the \textit{lengths of bit strings} of codewords from $\mathcal{C}_{\lambda}$, which provides a fresh and structured way to encode combinatorial invariants associated with partitions, numerical semigroups and finite Abelian groups.
11:10 AM – 11:30 AM 115-C Short Communications

Description of Right (Left) Rickart Algebras

When Rickart introduced the concept of B$^*_p$-algebra, he used left and right annihilators. Later, Kaplansky in his work called B$^*_p$-algebras Rickart C$^*$-algebras. For Rickart C$^*$-algebras, it was unimportant which annihilator to use, left or right. To find the difference between using left and right annihilators, it was necessary to expand the class of the algebraic structures under consideration. This was done in 1960 by A. Hattori. A. Hattori introduced the concept of a right p.p. ring, as a ring in which each principal left ideal is projective. It was later proved that right p.p. rings are precisely left Rickart rings.The chosen notions were built around a right (left) annihilator. For each nonempty subset $\mathcal{S}$ of an associative ring $\mathcal{R}$, the right (left) annihilator of $\mathcal{S}$ is defined by $\mathcal{S}^r:=\{a\in \mathcal{R}: sa={\bf 0}, \,\, \forall s\in \mathcal{S}\}$ (resp. $\mathcal{S}^l:=\{a\in \mathcal{R}: as={\bf 0}, \,\, \forall s\in \mathcal{S}\}$). Thus, an associative ring $\mathcal{R}$ is called a right (left) Rickart ring if, for each element $a\in \mathcal{R}$, there exists an idempotent $e\in \mathcal{R}$ such that $\{x\}^r=e\mathcal{R}$ (resp. $\{x\}^l=\mathcal{R}e$).Our study of the algebra-theoretic analogue of Rickart C$^*$-algebras is based on the following definition: an associative algebra that is a right (left) Rickart ring is called a right (resp. left) Rickart algebra.In our paper, we provide a criterion for some associative algebras to be a right (left) Rickart algebra. Namely, we prove that an associative algebra $\mathcal{A}$ with an idempotent $p$ and a nonzero nilpotent radical $\mathcal{N}$ such that $\mathcal{A}=\mathbb{F}p\dot{+}\mathcal{N}$ is a right Rickart algebra if and only if, for any nonzero $a$, $b\in\mathcal{N}$, $ab=0$, $pa=a$ and $ap=0$. And we prove that, an associative algebra $\mathcal{A}$ with mutually orthogonal idempotents $p$, $q$ and a nilpotent radical $\mathcal{N}\neq \{0\}$ such that $\mathcal{A}=\mathbb{F}p\dot{+}\mathbb{F}q\dot{+}\mathcal{N}$ is a right Rickart algebra if and only if $p+q$ is a left unit of $\mathcal{A}$, $p\mathcal{N}p=\{0\}$, $q\mathcal{N}q=\{0\}$, $q\mathcal{N}p=\{0\}$, and, for any $a\in q\mathcal{N}$ such that $a(p+q)=0$, andfor any $b\in p\mathcal{N}q$, from $a\neq 0$, $b\neq 0$ it follows that $ab\neq 0$. Theorems symmetric to these theorems hold for left Rickart algebras.
11:10 AM – 11:30 AM 118-C Short Communications

On a Perturbed Critical Semilinear Equation with Singularity

In this poster, I will discuss necessary and sufficient conditions on the perturbation $\rho$ for the existence of positive least energy solutions of the critical singular semilinear elliptic equation $ -\Delta u = \frac{|u|^{2^{*}(s)-2}}{|x|^s}u + \rho(u) $ with Dirichlet boundary condition in a bounded smooth domain in $\mathbb R^n$ containing the origin, where $2^*(s)=\frac{2(n-s)}{n-2}$ with $0\leq s<2$. Moreover we show that the almost necessary and sufficient condition obtained for the case $s=0$ in [1] differs conceptually when $0
11:10 AM – 11:30 AM 115-B Short Communications

Simulating Blood Flow Dynamics Across Planetary Gravity Variations Using Physics-Informed Neural Networks

In this study, we have analyzed the effects of simulated gravity variations for different planets on blood flow using numerical and machine learning techniques. Although it has already been experimentally proven that the vascular resistance and cardiac output are affected by gravitational variations, proper mathematical modelling and simulation of blood flow under variable gravity conditions for different planets has not been done. The present study addresses this gap by investigating blood flow dynamics under Earth (1g), Mars (0.38g), Moon (0.16g), microgravity (0g), and hypergravity conditions (2g, 3g). A deep learning-based Physics-Informed Neural Network (PINN) is employed to solve the governing equations of blood flow under these diverse gravitational environments. The PINN model is validated against the Keller box method (KBM), showing minimal discrepancy across all gravity scenarios. Absolute error simulations demonstrate that higher numbers of hidden layers and neurons produce more accurate results that closely match KBM output for each gravitational condition. Graphical representations of blood flow velocity and wall shear stress (WSS) are provided for different influencing parameters across the gravity spectrum. The cases of microgravity and hypergravity are discussed and simulated in detail. Simulation results reveal that planetary-level gravity variations significantly influence blood flow patterns, with microgravity conditions showing purely pressure-driven flow characteristics. Simulation results reveal that increased amplitudes of the pressure gradient enhance blood flow velocity, while an elevated threshold heart pulse frequency reduces it. The outcomes showcase the high precision of the PINN model across diverse gravitational conditions, offering valuable insights for space medicine and terrestrial applications involving altered gravitational environments.
11:10 AM – 11:30 AM 115-A Short Communications

Topological Analysis of Changing Weighted Graphs Using Persistent Homology and THI

This paper studies how the shape of a weighted graph changes over time using tools from topological data analysis. At each moment, we construct a filtration from the edge weights and compute persistent homology to capture important structures, such as connected components and cycles. We use the Topological Homology Index (THI) to summarize the total strength of these structures into a single number. By looking at THI at different times, we can see when topological features appear, grow, or disappear. We also introduce simple measures that show how sensitive these features are to changes in the graph. This framework helps identify stable patterns and remove noise in many types of dynamic graphs or discrete data.
11:10 AM – 11:30 AM 116-A Short Communications

What Is Conformal Heat Flow?

In this presentation I will introduce the concept of conformal heat flow, which is originally designed to smoothing harmonic map flow. A conformal heat flow consists of evolution equations of map and metric of domain, where the metric evolves in conformal direction and depends on the energy density. We showed that the conformal heat flows of harmonic maps does not develop finite time singularity unlike original flow does.
11:30 AM – 11:50 AM 115-C Short Communications

A Computational Approach to Wedderburn Decomposition and Matrix Units in Rational Group Algebras

Let \( G \) be a finite group and \( \mathbb{Q}G \) its rational group algebra. Although the Wedderburn-Artin theorem ensures that \( \mathbb{Q}G \) decomposes as a finite direct product of matrix algebras over division algebras, obtaining this decomposition explicitly together with concrete matrix units for the simple components remains a challenging problem. Classical character theoretic methods determine primitive central idempotents, but they do not provide explicit realizations of the corresponding simple components. In this talk, we present a computational approach to the Wedderburn decomposition and a construction of matrix units in rational group algebras, based on Shoda pairs and their refinements. For a large class of monomial groups, this method yields an explicit description of a simple component as a matrix algebra over a crossed product algebra, thereby providing a constructive form of the Brauer-Witt theorem. We also illustrate how this approach can be applied to compute Schur indices over \( \mathbb{Q} \) for certain classes of finite groups. The results presented are based on recent joint work with Jyoti Garg and Gabriela Olteanu during 2023-2025.
11:30 AM – 11:50 AM 118-AB Short Communications

An Atomic Approach to Particular Solutions of Higher-Order Cauchy–Euler Equations

We present a recent and original contribution to the theory of higher-order non-homogeneous Cauchy–Euler differential equations. A new concept of atoms defined on finite sets of real numbers is introduced and used to construct explicit particular solutions without reducing the equation to constant-coefficient form. The proposed atomic method works directly in the original variable and exploits the intrinsic scaling structure of the Cauchy–Euler operator. In addition to exact solutions, the approach naturally yields accurate approximate particular solutions when only approximate roots of the characteristic polynomial are available. Theoretical convergence results are established, and numerical experiments confirm the stability and efficiency of the method. This work, provides a flexible analytical–numerical framework that complements classical techniques and is well suited for structured forcing terms and higher-order equations.
11:30 AM – 11:50 AM 118-C Short Communications

An Extended Quasi Two-Phase Mass Flow Model: Numerical Experiments and Physics-Informed Neural Networks (PINN) Architecture Design

The dynamics of solid-fluid mixture flows are strongly influenced by material composition and interactions with obstacles. We perform numerical experiments by varying the solid volume fraction, both with and without obstacles, employing an extended quasi-two-phase mass flow model. The employed model includes coupled mass and momentum balances equations together with virtual mass induced pressure-Poisson equation for bulk mixture flow and describes the new concepts of extended mixture viscosities, pressure, and velocities. These quantities are evolving functions of some dynamical variables, physical parameters, inertial and dynamical coefficients and the drift factors. The model incorporates a mobility induced pressure- and rate-dependent Coulomb viscoplastic deformation and sliding for the mixture, together with Dirichlet and von-Neumann boundary conditions for the numerical solution. The finite volume method is employed for discretization while Marker-and-cell method is used for visualization. Our simulation approaches are capable of acquiring the detailed interacting mixture velocities with obstacle, deposition, the flow over-topping, detachments off the bed, formation of avalanche jets and ballistic projection, and landing on the bed again. Moreover, PINN architecture is formulated by embedding the governing equations directly into the loss function of the neural network, thereby ensuring that the learned solutions remain consistent with the underlying physical laws. These simulations results can be applied in environmental engineering, geohazard mitigation particularly in the design of the defense structures in debris flow/ landslide prone zones.
11:30 AM – 11:50 AM 120-AB Short Communications

Hamiltonicity in Directed Toeplitz Graphs with $s_1=1$ and $s_2=3$

A directed Toeplitz graph $T_n\langle s_1,\dots,s_p;t_1,\dots,t_q\rangle$ with vertices $1, 2, \dots, n$, where the edge $(i,\,j)$ occurs if and only if $j-i=s_l$ or $i-j=t_k$ for some $1\leq l\leq p$ and $1\leq k\leq q$, is a digraph whose adjacency matrix is a Toeplitz matrix. In this talk, I discuss the hamiltonicity in directed Toeplitz graphs with $s_1=1$, $s_2=3$ and $s_3\leq 7$.
11:30 AM – 11:50 AM 115-A Short Communications

Primes and Absolutely or Non-Absolutely Irreducible Elements in Atomic Domains

An irreducible element of a commutative ring is called absolutely irreducible if none of its powers has more than one (essentially different) factorizations into irreducibles. Otherwise, the irreducible element is called non-absolutely irreducible. While absolute irreducibility has been studied in various contexts, including the study of number fields and class groups, its investigation in the theory of non-unique factorization of domains is still limited.Not all absolutely irreducible elements are prime, and certain domains exhibit striking extremes: either all irreducibles are absolutely irreducible, or none are. In this talk, we discuss integral domains that realize each of the eight logically possible scenarios concerning the existence or non-existence of primes, absolutely irreducibles that are not prime, and irreducible elements that are not absolutely irreducible. These constructions highlight the diversity of factorization behavior in commutative algebra and give new insights into the structure of integral domains.
11:30 AM – 11:50 AM 119-AB Short Communications

Probabilistically Nilpotent Finite Groups

There are many ways to characterize finite nilpotent groups. For example, a finite group $G$ is nilpotent iff all long commutators in $G$ are trivial, or iff any two Sylow subgroups of coprime orders commute, and so on.In this talk we will discuss finite groups in which one of suchfeatures holds with high probability and we will see how this affectsthe structure of the group.
11:30 AM – 11:50 AM 116-A Short Communications

Statistical Soliton on Statistical Poisson Warped Product Space

In this article, we first define the concept of a statistical Poisson manifold. We then explore the structure of Einstein statistical Poisson warped product spaces. Following this, we introduce the notion of a statistical soliton on a statistical Poisson warped product space and provide a detailed discussion of its properties.Next, we establish a version of Chen's inequality for immersed statistical Poisson warped product submanifolds within a statistical Poisson manifold of constant sectional curvature. We also derive the dual Einstein gravitational equations and the dual contravariant Einstein equations for contravariant Lorentzian statistical Poisson warped product spaces.Furthermore, we define the concept of a contravariant Poisson space-time warped product space with a potentially infinite cometric, and then examine the corresponding contravariant statistical Poisson space-time warped product space in detail.
11:30 AM – 12:30 PM Terrace Ballroom Plenary Lecture

The KPZ Fixed Point

We describe some of the mathematics which has developed in the last quarter century out of the study of one dimensional random growth models.
11:30 AM – 11:50 AM 115-B Short Communications

Wave Propagation on a Fluid-Filled Cylindrical Shell

A mathematical investigation of the dynamic characteristics of a cylindrical shell in the presence of an internal fluid is presented. The velocity potential of the internal compressible fluid is obtained through the Helmholtz equation and is subject to the impenetrable boundary. The pressure at the interior of the shell in the presence of the fluid is obtained by inserting the asymptotic solution of the Helmholtz equation into the linearized Bernoulli equation. The kinematics of the shell is governed by the Sanders-Koiter thin shell theory. The implementation of the asymptotic integration technique onto the equations of motion and the general dispersion relation for a propagating wave on a circular cylindrical shell enables the extraction of each frequency mode under a small value of thickness-to-curvature ratio. The condition of the existence of a non-degenerate dynamics edge effect is examined by the implementation of the asymptotic method at a particular edge of the considered shell. Analytical and numerical analysis of the resulting dispersion relation is performed, and the results are illustrated with their underlying physics.
11:50 AM – 12:10 PM 115-B Short Communications

A Game-Theoretic Quantum Algorithm for Solving Magic Squares

Variational quantum algorithms (VQAs) offer a promising near-term approach to finding optimal quantum strategies for playing non-local games. These games test quantum correlations beyond classical limits and enable entanglement verification. In this work, we present a variational framework for the Magic Square Game (MSG), a two-player non-local game with perfect quantum advantage. We construct a value Hamiltonian that encodes the game's parity and consistency constraints, then optimize parameterized quantum circuits to minimize this cost. Our approach builds on the stabilizer formalism, leverages commutation structure for circuit design, and is hardware-efficient. Compared to existing work, our contribution emphasizes algebraic structure and interpretability. We validate our method through numerical experiments and outline generalizations to larger games.
11:50 AM – 12:10 PM 118-AB Short Communications

An Optimal Iterative Family for Solving Multiple Roots of Nonlinear Equations

In this study, we develop a new family of fourth-order iterative methods for the numerical solution of nonlinear equations possessing multiple roots. It is well known that many optimal higher-order schemes suffer from severe instability or loss of convergence when the first derivative vanishes or becomes extremely small in the neighbourhood of the root. The proposed iterative family effectively overcomes this drawback while preserving an optimal fourth-order convergence rate for roots of arbitrary multiplicity. A rigorous local convergence analysis is carried out to establish the theoretical validity of the method and to confirm its fourth-order convergence. Furthermore, extensive numerical experiments involving benchmark problems from applied science and engineering are presented to assess the performance of the proposed scheme. The results demonstrate superior accuracy, efficiency, and robustness when compared with existing methods. In particular, the proposed family exhibits reliable convergence even in the critical case where f′(x) = 0 or is nearly zero near the solution, a scenario in which many classical and modern techniques fail. Consequently, the proposed methods constitute a robust and efficient computational framework for solving nonlinear equations with multiple roots.
11:50 AM – 12:10 PM 116-A Short Communications

Holonomy of the Obata Connection on 2-step Hypercomplex Nilmanifolds

We study the holonomy of the Obata connection on 2-step hypercomplex nilmanifolds. By explicitly computing the curvature tensor, we determine the conditions under which the Obata connection is flat, showing that this depends on the nilpotency step of each complex structure. In particular, we show that the holonomy algebra of the Obata connection is always an abelian subalgebra of \(\mathfrak{sl}(n, \mathbb{H})\): to establish this, we prove the \(\mathbb{H}\)-solvable conjecture for 2-step hypercomplex nilmanifolds. Furthermore, we provide new examples of $k$-step nilpotent hypercomplex nilmanifolds, with arbitrary $k$, which are not Obata flat.
11:50 AM – 12:10 PM 118-C Short Communications

Invariant Solutions of Fuzzy Fractional Vibration Equations

In this work, we consider one dimensional fuzzy fractional vibration equation with large membrane,\\\[\begin{eqnarray*}\frac{1}{\tilde{c}^2} \frac{\partial^{\beta}\tilde{v}}{\partial t^{\beta}}=\frac{\partial^2 \tilde{v}}{\partial x^2} + \frac{1}{x} \frac{\partial \tilde{v}}{\partial x}; 1<\beta \leq 2, t>0, x \in [0, 1],\end{eqnarray*}\]with\[\begin{eqnarray*}\tilde{v}(x,0)=\tilde{p}(x), \ \ \ \tilde{v}'(x, 0)=\tilde{c}\tilde{q}(x),\end{eqnarray*}\]where, $\frac{\partial^{\beta}}{\partial t^{\beta}}$ is a Caputo fractional derivative. Scaling transformation is used to transform the fuzzy fractional vibration equation into the second order fuzzy fractional ordinary differential equation with variable coefficients. Invariant solutions are derived by solving the second order fuzzy fractional differential equations. Finite difference scheme is used to establish the numerical results. Examples are presented in detail.
11:50 AM – 12:10 PM 120-AB Short Communications

Marangoni Convection and Instability Near the Air-Liquid Interface

In this presentation, steady thermo- and solute-capillary convection, instability, and pattern evolution near the air-liquid interface driven by point heat and mass sources are investigated. First, under the assumption of the conically similar viscous flow, an exact axi-symmetric solution of the steadythermo- and soluto-capillary convection near the air-liquid interface is determined due to the constant heat and mass fluxes. It is shown thatthe constant heat, mass fluxes, and the radial surface tension cause the divergent motion at the interface and the Marangoni convectionbeneath the interface. Then, the linear stability of the steady thermo- and soluto-capillary convection in response to the azimuthal disturbanceis analyzed. At a given Peclet (or Schmidt), Marangoni (or Prandtl), and elasticity numbers, the steady basic flow loses its stability whenReynolds number is beyond the critical value. The critical patterns of the velocity fields and the isothermal, iso-concentration lines in the three-dimensional flow system in response to the disturbance harmonic wave number are dominated by both the radial and azimuthal surface tensions. This research is supported by the National Science Foundation through the Grants Nos. 11172310, 11472284 and 12272384.
11:50 AM – 12:10 PM 115-C Short Communications

On Finite Groups Defined by Conjugacy Relations and Character Fields

For a finite group $G$, the conjugacy classes in $G$ and the irreducible characters of $G$ are both topics of fundamental interest and are closely related to each other as well as to the structure of $G$. Some classes of groups, for instances rational groups and real groups are based on the character values of irreducible characters of $G$, and are equivalently defined by the conjugacy criterion satisfied by elements in $G$. Lately, some interesting generalisations of rational groups have been recognised, of which some are related to the central units of integral group ring of $G$. In this short communication, I will give a brief overview of these classes, which will also demonstrate the relationship between the conjugacy relations in $G$ and its character fields. I will demonstrate some recent progress on problems related to some of these classes.
11:50 AM – 12:10 PM 115-A Short Communications

Some Theoretical Foundation for Protein Identification Through Cyclic Codes

In recent work, the possible relationship between protein synthesis processes and digital transmission systems has been successfully investigated. Advances in this area could lead to conclusions about evolution and the connection between species. Based on the Code Theory, biological sequences have been identified as BCH code words to verify the validity of this model. In the article Construction of Cyclic Codes over Z20 for Identifying Proteins [1], three algorithms were designed to identify odd-length biological sequences of amino acids as keywords of cyclic codes. In this talk, we will present some aspects of the mathematical background of the algorithms through which we have been able to detect possible improvements for some steps of the above-mentioned algorithms.1. Galíndez Gómez, V., Duarte González, M.E. (2019). Construction of Cyclic Codes over Z20 for Identifying Proteins. In: Figueroa-García, J., Duarte-González, M., Jaramillo-Isaza, S., Orjuela-Cañon, A., Díaz-Gutierrez, Y. (eds) Applied Computer Sciences in Engineering. WEA 2019. Communications in Computer and Information Science, vol 1052. Springer, Cham. https://doi.org/10.1007/978-3-030-31019-6_4
11:50 AM – 12:10 PM 119-AB Short Communications

Zero Dynamics for a Class of Robustly Stable Polynomials

In this contribution, we introduce two different methods to construct robustly stable Schur polynomials that depend on an uncertain parameter, by using basic properties of orthogonal polynomials on the unit circle. We also develop a procedure to describe the behavior of the zeros of a class of uncertain polynomials with respect to the uncertain parameters. Some illustrative examples are presented.
12:10 PM – 12:30 PM 118-AB Short Communications

An Arrow–Hurwicz–Inspired Finite Element Approach for Steady Navier–Stokes and MHD Equations Without Saddle-Point Solvers

We propose a new Arrow–Hurwicz-type finite element method for the numerical approximation of the steady incompressible Navier–Stokes and MHD equations. The method is motivated by artificial compressibility techniques commonly used for unsteady flows and is designed to avoid the solution of saddle-point systems arising from the incompressibility constraint. Rigorous analysis is carried out, establishing uniform boundedness of the discrete solutions and convergence to the exact solution under a standard small-data assumption ensuring uniqueness. In addition, a two-grid variant of the proposed algorithm is introduced to further enhance computational efficiency. Numerical experiments demonstrate that the method achieves a significant acceleration in convergence compared to classical approaches, while maintaining accuracy and incurring no additional computational cost.
12:10 PM – 12:30 PM 120-AB Short Communications

Cellular Automata with a Unique Active Transition

For any group $G$ and any set $A$, let $A^G$ be the set of all functions $x : G \to A$. A cellular automaton (CA) over $A^G$ is a transformation $\tau : A^G \to A^G$ such that there exists a finite neighborhood $S \subseteq G$ and a local function $\mu : A^S \to A$ satisfying \[ \tau(x)(g) = \mu( (g \cdot x)\vert_{S}), \quad \forall x \in A^G, g \in G, \]where $g \cdot x \in A^G$ denotes the shift action of $G$ on $A^G$ given by $(g \cdot x)(h) := x(hg)$, for all $x \in A^G$, $g,h \in G$. The classical setting, which has been widely studied from a dynamical and computational perspective, occurs when $G = \mathbb{Z}^d$, $d \in \mathbb{N}$, and $A= \{ 0,1 \}$. We say that a CA $\tau : A^G \to A^G$ has a unique active transition if there exists a local defining function $\mu : A^S \to A$ for $\tau$ and a pattern $p \in A^S$ such that, the group identity $e$ is in $S$ and for all $z \in A^S$,\[ \mu(z) = z(e) \ \Leftrightarrow \ z \neq p. \]Intuitively, a CA with a unique active transition acts on $A^G$ almost as the identity function, except when it reads a fixed pattern $p \in A^S$. We write $\tau_p^a$ for a CA with unique active transition $p \in A^S$ and $a:=\mu(p) \in A$. In recent joint work with M. G. Magana-Chavez, E. Veliz-Quintero, and L. de los Santos Banos, we noticed that if $p \in A^S$ is constant or symmetric (i.e., $S=S^{-1}$ and $p(s) = p(s^{-1})$, $\forall s \in S$), then $\tau_p^a$ is idempotent (i.e., $(\tau_p^a)^2 = \tau_p^a$), and we obtained a full characterization of the idempotency of $\tau_p^a$ when $p$ is quasi-constant (i.e. there exists $s \in S$ such that $p \vert_{S \setminus \{s\}}$ is constant). Moreover, when $G=\mathbb{Z}$ and $S$ is a finite interval of $\mathbb{Z}$ such that $0 \in S$, we showed that $\tau_p^a$ is either idempotent or strictly almost equicontinuous as a dynamical system, and we completely characterized each one of these situations in terms of $p$. However, there are still many open problems regarding this class of cellular automata, such as a full characterization of their idempotency for arbitrary $G$ and $p \in A^S$.
12:10 PM – 12:30 PM 116-A Short Communications

Eta-Ricci-Bourguignon Solitons on Three-Dimensional H-Paracontact Manifolds

This work explores the geometric properties of Eta-Ricci-Bourguignon solitons and their gradient counterparts within the framework of 3-dimensional H-paracontact manifolds. Our main focus lies in characterizing these solitons through the structural behavior of the associated operator h. To complement our theoretical results, we also construct examples that demonstrate the validity and applicability of our results.
12:10 PM – 12:30 PM 118-C Short Communications

Existence of Weak Solutions to Nonlinear Drift–Diffusion Equations and Applications

In this presentation, we discuss recent existence results for nonlinear diffusion equations, including the porous medium and parabolic p-Laplace equations, with a divergence-type drift term. These results are broadly applicable to reaction–diffusion systems, including Keller–Segel models. We emphasize the identification of scaling-invariant functional classes for the drift, depending on the nonlinear diffusion and the boundary data.
12:10 PM – 12:30 PM 115-A Short Communications

Nonlinear Dynamics of a Ratio-Dependent Population System: Stability Analysis, Bifurcations and Chaotic Behavior

We present the complex dynamics of a prey-predator system modeled using a Leslie-type framework. The analysis begins with an examination of the system’s stability properties. This is followed by an exploration of bifurcation phenomena and the emergence of chaotic behavior within the model. To validate and extend the theoretical analysis, numerical simulations are performed. The findings are subsequently interpreted from a biological perspective, emphasizing their ecological relevance.
12:10 PM – 12:30 PM 115-B Short Communications

On Cilleruelo-Nathanson's Method in Sidon Sets

A set $A$ of integers is defined as a Sidon set if all the sums $a+a'$, $a\le a'$, $a,a'\in A$ are distinct. In 2022, Nathanson further considered Sidon sets for linear forms. In this talk, we will present our recent results on generalized Sidon sets.
12:10 PM – 12:30 PM 115-C Short Communications

On Zero-Divisor Graph for the Factor Rings and Its Metric Dimension

This study pertains to the metric dimension of the zero-divisor graph (ZDG) $\Gamma(R)$ for the factor ring $R = \mathbb{Z}_{p^2}[y]/\langle y^2 \rangle$, where $p \ge 3$ is a prime number. The ZDG is constructed using the zero-divisors of this ring. We first characterize the set of zero divisors $Z(R)$ and analyze the structure of the graph, confirming its diameter is 2.\\ Metric dimension of the ZDG $\Gamma(\mathbb{Z}_{p^2}[y]/\langle y^2 \rangle)$ has been computed by analyzing how its $p^3-1$ vertices partition into twin equivalence classes ($T$), which represent vertices undifferentiable by distance. The findings reveal a critical dependence on the prime $q$: for the minimal case, $\mathbf{p=3}$, the complex algebraic structure leads to \[ \dim(\Gamma(\mathbb{Z}_{9}[y]/\langle y^2 \rangle)) = \mathbf{21}. \] However, for all primes $\mathbf{p \ge 5}$, the structure simplifies and the metric dimension follows to the general formula \[ \dim(\Gamma(\mathbb{Z}_{p^2}[y]/\langle y^2 \rangle)) = \mathbf{p^3 - 2p - 1}. \] This clear difference between the linear increase of $T$ ($\mathbf{2p}$ classes) and the cubic expansion of vertices validates the graph's huge symmetry and explains why its metric dimension is still very high, almost equal to the entire number of vertices.\\ The finding that $p=3$ is an exceptional case \[ \dim(G)=21 \quad \text{vs.} \quad p^3 - 2p - 1 = 3^3 - 2(3) - 1 = 27 - 7 = 20 \] highlights that the algebraic properties of $\mathbb{Z}_{9}[y]/\langle y^2 \rangle$ are fundamentally different from those of $\mathbb{Z}_{p^2}[y]/\langle y^2 \rangle$ for $p \ge 5$, despite their visual similarity.\\ A MATLAB Code for the zero-divisor graph has also been discussed.\\ \noindent\textbf{MSC(2020):} 05C10, 05C12, 05E40.\\
12:10 PM – 12:30 PM 119-AB Short Communications

Support of Semiclassical Measures in Higher Dimensions

A central question in quantum chaos is how classical chaotic dynamics influence quantum behavior. On compact Support of Semiclassical measures in higher dimensions manifolds, pure quantum states correspond to Laplacian eigenfunctions. The quantum unique ergodicity (QUE) conjecture of Rudnick and Sarnak predicts that on hyperbolic manifolds, all high-energy eigenfunctions become uniformly distributed. The asymptotic behavior of eigenfunctions can be formulated in terms of semiclassical measures, which describe the microlocal distribution of eigenfunction mass. One approach towards the QUE conjecture applies microlocal analysis and uncertainty principles to characterize the support of semiclassical measures. I will discuss recent work that uses the breakthrough higher-dimensional fractal uncertainty principle of Cohen. Using this uncertainty principle, we prove the first result on the support of semiclassical measures on real hyperbolic n-manifolds. This is joint work with Nicholas Miller.
12:30 PM – 12:50 PM 120-AB Short Communications

Binary Code Generated by the Hyperbolic Quadrics of a Symplectic Polar Space of Even Order

Let $V$ be a vector space of dimension $2n$, $n\geq 2$, defined over the finite field of order $q$ and let $f$ be a nondegenerate alternating bilinear form on $V$. Denote by $W(2n-1,q)$ the symplectic polar space of rank $n$ associated with $(V,f)$.Suppose that $q$ is even. A nonsingular quadric in $\mbox{PG}(2n-1,q)$ with quadratic form $\kappa$ is called a quadric of $W(2n-1,q)$ if $f$ equals the polarization $f_{\kappa}$ of $\kappa$ defined by$f_{\kappa}(\bar{v},\bar{w})=\kappa(\bar{v}+\bar{w})-\kappa(\bar{v})-\kappa(\bar{w})$ for $\bar{v},\bar{w}\in V$.Under the action of the projective symplectic group $\mbox{PSp}(2n,q)$, the set of all quadrics of $W(2n-1,q)$ splits into two orbits: the set of all hyperbolic quadrics of $W(2n-1,q)$ and the set of all elliptic quadrics of $W(2n-1,q)$. Let $\mathcal{H}$ denote the binary code generated by the hyperbolic quadrics of $W(2n-1,q)$. It is known that $\mathcal{H}$ equals the binary code generated by the elliptic quadrics of $W(2n-1,q)$. In this talk, we characterize the codewords of minimum and maximum weights in $\mathcal{H}$ and its dual code $\mathcal{H}^\perp$.This is a joint work with Devjyoti Das, Bart De Bruyn and N. S. Narasimha Sastry.
12:30 PM – 12:50 PM 120-AB Short Communications

Enumeration of Domino Tilings of Certain Planar Regions on the Square Lattice

Over the years, combinatorialists have been interested in enumerating tilings of certain finite regions on the plane. For instance, the number of lozenge tilings of a regular hexagon on the triangular lattice is known due to the work of MacMahon, while the number of domino tilings of an Aztec Diamond on the square lattice is known due to the work of Elkies, Kuperberg, Larson, and Propp.These two results have inspired mathematicians over the years to explore related questions and study more general regions on the plane. We continue this direction of study and prove several exact enumeration formulas for domino tilings of certain planar regions, which are generalizations of Aztec diamonds. In particular, we prove exact enumeration results for Double Aztec Rectangles and generating function results for quartered Aztec Diamonds. Our work generalizes several known results.
12:30 PM – 1:30 PM Benjamin Franklin Stage Films @ ICM

Lobachevsky Space

Film Directed by Ekaterina Eremenko

Like in Lobachevsky geometry where the space is in excess and the lines behave unusually, in the film "Lobachevsky space" unusual mathematics is spiced up by a good portion of background history and current politics. Past and present, science and politics, Russia and Germany, Lobachevsky and Gauss are confronted in a polyphonic dialogue. A modern portrait of a lonely genius, rector of the Kazan University, whose pioneering ideas forestalled the development of mathematics and science in general. Lobachevsky's story reemerges through the observation of the daily life of scientists in Kazan, Berlin and Göttingen.

Source: Discretization in Geometry and Dynamics

12:30 PM – 1:30 PM Breaks

Lunch on Own

12:30 PM – 12:50 PM 116-A Short Communications

Mathematical and Computational Modeling of the Population Dynamics of Aedes Aegypti

Aedes aegypti is the primary vector responsible for the transmission of dengue, Zika, chikungunya, and yellow fever. Effective control strategies require a detailed understanding of the mosquito spatial population dynamics, including its life cycle. Most existing mathematical models describe only the total mosquito population, which limits their ability to capture spatial effects that are crucial from a public health perspective.In this talk, we present a framework for modeling the spatial population dynamics of Aedes aegypti using partial differential equations. The proposed models incorporate the mosquito life cycle and are analyzed under both homogeneous and heterogeneous scenarios, where model parameters may depend on topography and distinguish between urban features such as streets, houses, and green areas. Analytical relationships are derived linking the carrying capacity of the aquatic phase to experimentally measurable quantities, such as the maximum number of female mosquitoes, eggs, and larvae.The methodology is applied to different insecticide-based control strategies. For example, numerical simulations suggest that weekly insecticide applications are the most effective method for population control. Moreover, in heterogeneous environments, mosquito populations tend to remain confined within residential blocks, limiting the effectiveness of insecticide-based interventions. Another example focuses on the release strategies for genetically modified mosquitoes. The model allows for the analytical determination of critical release frequencies and the quantity required for population suppression. All analytical predictions are validated through computational simulations, and the optimal release frequencies are shown to be consistent with values reported in the literature.
12:30 PM – 12:50 PM 118-AB Short Communications

Multi-Dimensional Bohr Radii of Banach Space Valued Holomorphic Functions

We studied the multi-dimensional Bohr radii of holomorphic functions defined on the Banach sequence spaces with values in the Banach spaces. For the case of finite-dimensional Banach spaces, we exhibited the exact asymptotic growth of the Bohr radius. To achieve our goal in the finite case, we used $\ell_{p'}$-summability of certain coefficients of a given polynomial in terms of its uniform norm on $\ell_p^n$. The infinite case is handled using the techniques developed in recent years from the work of Defant, Maestre and Schwarting. We crucially used several properties of the symmetric $M$-linear mapping associated with a homogeneous polynomial of degree $M$ in our analysis. Furthermore, we studied the bounds of the arithmetic Bohr radius of Banach space-valued holomorphic functions defined on the Banach sequence spaces, which generalises the work of Defant, Maestre, and Prengel in this direction.
12:30 PM – 12:50 PM 115-B Short Communications

Roth's Theorem in Super Smooth Numbers

We say that the set of $y$-smooth numbers $\mathcal{S}(N,y)$ up to $N$ is super smooth if $y=\log^KN$ for a large fixed constant $K$. We show that the Roth's theorem on arithmetic progressions is true in super smooth numbers case. This extends the result of Harper where he showed the statement is true under a weaker hypothesis.
12:30 PM – 12:50 PM 118-C Short Communications

Stokes Phenomenon in Cauchy-Riemann Geometry

This work is related to remarkable connections between CR (Cauchy-Riemann) geometry and the theory of Dynamical Systems, recently developed in my joint work with R.Shafikov, B.Lamel, L.Stolovitch, and P.Ebenfelt (the CR - DS method).{\it CR geometry} is the geometry of embedded real submanifolds in a complex manifold (CR submanifolds) endowed with the induced complex structure on their complex tangent bundle. It originated in the 1907 work of Poincare on the Riemann Mapping Theorem in SCV, and was further developed in the fundamental work of E.Cartan, Tanaka, Chern and Moser. {\it Stokes phenomenon} for classes of dynamical systems means those systems exhibiting different geometric behavior in various sectorial domains associated with a stationary point. Transformations of such systems to a simpler model with the given asymptotics may vary depending on the sector, which results in the appearance of a nontrivial transition cocycle (Stokes cocycle). The latter is a geometric invariant of the dynamical system "invisible" from the point of view of formal power series classification. Stokes Phenomenon shows up for such important classes of dynamical systems as saddle-node singularities of vector fields and parabolic singularities of diffeomorphisms.A typical phenomenon of Cauchy-Riemann geometry is the analytic hypoellipticity: formal or smooth transformations of analytic CR manifolds are analytic too, for large classes of CR manifolds. However, in a number of recent publications (e.g. [JEMS2016], [JDG2016], [AJM2018], [AIM22]) we demonstrated the failure of the analytic hypoellipticity for classes of CR manifolds. This raised a key question on their actual analytic classification.In this joint work with L.Stolovitch, we discover that the CR classification problem here falls into the scope of Stokes Phenomena. For a general class of CR manifolds (infinite type hypersurfaces in complex 2-space), we show the existence of an in general nontrivial transition (Stokes) cocycle uniquely associated with an infinite type point. Two CR manifolds appear to be equivalent iff they are formally equivalent and their Stokes cocycles coincide. Our approach relies on the above mentioned CR - DS method, and the Multisummabilty Theory for solutions of differential equations (developed in earlier work of Balser, Braaksma, Ecale, Malgrange, Ramis, Sibuya).Our outcome gives probably the first description of Stokes Phenomenon for geometric structures on manifolds.
12:30 PM – 12:50 PM 115-C Short Communications

Toward a Mathematical Theory of Deep Learning: Lessons from Personal Research

A century ago, breakthroughs like relativity and quantum mechanics emerged from or developed alongside rigorous mathematical theories. Today's AI revolution presents a stark contrast: progress remains predominantly empirical while mathematical theory lags significantly behind. In this short communication, I will share perspectives on current efforts to establish theoretical foundations for deep learning, drawing from my personal research experiences. We will examine the strengths and limitations of various approaches---including toy models, phenomenological models, and conditional-theory approaches---and explore why certain methods succeed in capturing specific behaviors while failing to provide comprehensive understanding. The short communication concludes by highlighting opportunities for the mathematics community to contribute to advancing the theoretical foundations of deep learning.
12:30 PM – 12:50 PM 115-A Short Communications

Traveling Wave Solutions in a Delayed Hybrid Reaction-Diffusion and Difference SIR Epidemic Model with Protection Phase

We consider a general class of diffusive Kermack-McKendrick SIR epidemic models with an age-structured protection phase with limited duration, for example due to vaccination or drugs with temporary immunity. The characteristics method reduces the model to a coupled system of a reaction-diffusion equation and a continuous difference equation with a time-delay and a nonlocal spatial term caused by individuals moving during their protection phase. We study the existence and non-existence of non-trivial traveling wave solutions. We get almost complete information on the threshold and the minimal wave speed that describes the transition between the existence and non-existence of non-trivial traveling waves that indicate whether the epidemic can spread or not. We discuss how model parameters, such as protection rates, affect the minimal wave speed. The difficulty of our model is to combine a reaction-diffusion system with a continuous difference equation. By using the Schauder's fixed point theorem, we reduce the problem of the existence of non-trivial traveling wave solutions to the existence of an admissible pair of upper and lower solutions.
12:30 PM – 12:50 PM 119-AB Short Communications

Well-Posedness and the ŁOjasiewicz-Simon Inequality in the Asymptotic Analysis of a Nonlinear Heat Equation with Constraints of Finite Codimension

We establish the global well-posedness of the $D(A)-$valued strong solution to a nonlinear heat equation with constraints on a Poincaré domain $\mathcal{O}\subset \mathbb{R}^d$ whose boundary is of class $C^2$. Consider the following nonlinear heat equation\[\begin{align*} \frac{\partial u}{\partial t} - \Delta u + |u|^{p-2}u = 0,\end{align*}\]projected onto the tangent space $T_u\mathcal{M}$, where $\mathcal{M}:=\left\{u\in L^2(\mathcal{O}):\|u\|_{L^2(\mathcal{O})}=1\right\}$ is a submanifold of $L^2(\mathcal{O})$. The nonlinearity exponent satisfies $2\le p < \infty$ for $1\leq d\leq 4$ and $2 \le p \le \frac{2d-4}{d-4}$ for $d \ge 5$. The solution is constrained to lie within $\mathcal{M}$, which encodes the norm-preserving constraint. By modifying the nonlinearity and exploiting the abstract theory for $m-$accretive evolution equations, we prove the existence of a global strong solution. Using the resolvent-idea and the Yosida approximation method, we derive regularity results. In the asymptotic analysis, $\mathcal{O}$ is restricted to bounded domains with even $p$ and $1\le d \le 3$. For any initial data in $D(A) \cap \mathcal{M}$, we apply the Łojasiewicz-Simon gradient inequality on a Hilbert submanifold, to demonstrate that the unique global strong solution converges in $W^{2,q}(\mathcal{O}) \cap W^{1,q}_0(\mathcal{O})$ to a stationary state, where $2 \le q < \frac{2d}{d + 4 - 4\beta}$ and $1 < \beta < \frac{3}{2}$. This work proposes an alternative method for establishing the global existence and analyzing long-term behavior of the unique strong solution to an $L^2-$norm preserving nonlinear heat equation.It is a joint work with Zdzisław Brzeźniak, Manil T. Mohan and Piotr Rybka.
12:50 PM – 1:10 PM 118-C Short Communications

A Hybrid High-Order Finite Element Method for a Nonlocal Nonlinear Problem of Kirchhoff Type

We present a hybrid high-order (HHO) finite element method for a class of nonlocal nonlinear problems of Kirchhoff type. The proposed method supports arbitrary-order polynomial approximations on structured and unstructured polytopal meshes. We prove well-posedness of the resulting nonlinear discrete problem and establish optimal-order convergence in a discrete energy norm. The nonlinear system is solved using Newton’s method applied to a sparse matrix system. Numerical experiments are presented to validate the theoretical results.
12:50 PM – 1:10 PM 118-AB Short Communications

Asymptotic Value of the Multidimensional Bohr Radius

In this talk, I will discuss the exact asymptotic value of the Bohr radii and the arithmetic Bohr radii for the holomorphic functions defined on the unit ball of the $\ell_p^n$ space and having values in the simply connected domain of $\mathbb{C}$. Moreover, I will present the sharp Bohr radius for four distinct categories of holomorphic functions. These functions map the bounded balanced domain $G$ of a complex Banach space $X$ into the following domains: the right half-plane, the slit domain, the punctured unit disk, and the exterior of the closed unit disk.
12:50 PM – 1:10 PM 119-AB Short Communications

Energy Decay Analysis in Coupled Systems with Fractional Derivative Damping: A Numerical and PINN Approach

Abstract: This study investigates the energy decay behavior of coupled dynamical systems incorporating fractional derivative damping. We first establish the governing equations of motion for a coupled system with fractional-order viscoelastic damping and analyze its theoretical energy decay properties. A numerical scheme based on finite differences and spectral discretization is developed to validate the analytical results and to study the influence of fractional parameters on system stability. Additionally, a Physics-Informed Neural Network (PINN) framework is proposed to approximate the system dynamics and energy evolution without explicit discretization, offering a data-driven alternative for solving fractional differential equations. Comparative analyses between traditional numerical simulations and PINN predictions demonstrate strong agreement and highlight the efficiency of PINNs in capturing long-term decay trends.
12:50 PM – 1:10 PM 115-C Short Communications

Hotel Pricing with Spatial Impact: A Comprehensive Overview of Spatial Regression Models

Regression analysis is a common multivariate statistical method and mathematical model that is employed to understand the extent to which variables affect each other.Spatial regression is a highly effective method for understanding the effects of variables when location is hypothesised to have an impact on the location from which the data is collected. Yalcin and Mert conducted a study on nearly 1,500 data points in order to ascertain the characteristics affecting hotel prices, thereby demonstrating the efficacy of the location of the hotel [Determination of hedonic hotel room prices with spatial effect in Antalya, To appear in Economía, sociedad y territorio, 2018].The aim of this presentation is to provide a comprehensive overview of spatial regression models and the detection of spatial effects. The discussion will cover the construction of spatial weight matrices for the inclusion of spatial effects in models, as well as selection criteria for spatial models.All of the above topics will be explained using examples first presented in the paper by Yalcin and Mert.
12:50 PM – 1:10 PM 120-AB Short Communications

Isospectrality of Geometries Over Finite Rings

Let R be a Dedekind domain and $\mathfrak{p}\vartriangleleft R$ a prime ideal of finite index $p$. For any $r\in\mathbb{N}$, define $\mathcal{O}_{r}:={R}/{\mathfrak{p}^{r}}$, and let $\mathbb{P}_{\text{fr}}^{d}\left(\mathcal{O}_{r}\right)$ denote the flag complex on all free sub-modules of $\mathcal{O}_{r}^{d+1}$ with incidence relation. Two key examples to keep in mind are ${\mathbb{Z}}/{\left\langle p^{r}\right\rangle}$ and ${\mathbb{F}_{p}\left[t\right]}/{\left\langle t^{r}\right\rangle}$. The case $r=1$ is the classical projective finite geometry $\mathbb{P}^{d}\left(\mathbb{F}_{p}\right)$, which appears as the local vista of vertices in the Bruhat-Tits buildings of $PGL_{d}(\mathbb{Q}_{p})$ and $PGL_{d}(\mathbb{F}_{p}\left(\left(t\right)\right))$. The complex $\mathbb{P}_{\text{fr}}^{d}\left(\mathcal{O}_{r}\right)$ arises naturally when considering geodesic r-spheres in these buildings.Let $\mathbb{P}_{m,n}^{d}\left(\mathcal{O}_{r}\right)$ be the sub-graph induced by the free sub-modules of rank $m$ and $n$. In the first part of the talk we analyze the adjacency matrix of the square-graph of $\mathbb{P}_{1,n}^{d}\left(\mathcal{O}_{r}\right)$, and discover a structure that allows us to calculate their eigenvalues and, in particular, their spectral expansion. These eigenvalues are independent of the specific choice of $\left\{R,\mathfrak{p}\right\}$ and depend only on $\left\{ p,r,d\right\}$. Hence, for example, $\mathbb{P}_{1,n}^{d}\left({\mathbb{Z}}/{\left\langle p^{r}\right\rangle}\right)$ and $\mathbb{P}_{1,n}^{d}\left({\mathbb{F}_{p}\left[t\right]}/{\left\langle t^{r}\right\rangle}\right)$ are isospectral, and their square-graphs are even isomorphic. However, are the graphs themselves isomorphic?In the second part of the talk we discuss this question, and show how to distinguish between two such graphs using their automorphism groups. We prove a generalization of the Fundamental Theorem of Projective Geometry and find the automorphism group of $\mathbb{P}_{\text{fr}}^{d}\left(\mathcal{O}_{r}\right)$ and $\mathbb{P}_{m,n}^{d}\left(\mathcal{O}_{r}\right)$. We then use size considerations of the automorphism groups to show that $\mathbb{P}_{\text{fr}}^{d}\left({\mathbb{Z}}/{\left\langle p^{r}\right\rangle }\right)$ and $\mathbb{P}_{\text{fr}}^{d}\left({\mathbb{F}_{p}\left[t\right]}/{\left\langle t^{r}\right\rangle }\right)$ are not isomorphic (except for the case $p=r=2$, in which additional work is required).
12:50 PM – 1:10 PM 115-A Short Communications

On a Keller-Segel Type Equation to Model Brain Microvascular Endothelial Cells Growth's Patterns

In this talk, after briefly mentioning fundamental and practical mathematical questions which are important in the context of seeking new therapeutics for neurodegenerative diseases, I will focus on the following Partial Differential Equation (PDE) of Keller-Segel type,\[\begin{equation}(1)\left\{ \begin{array}{rl} u_t&=f(u)-b\nabla \cdot (u\nabla v)+d_u\Delta u \\ v_t&=cu-ev+d_v\Delta v \end{array} \right. \end{equation}\] Equation (1) can reproduce two dimensional patterns which are typically observed in vitro under microscopy during brain microvascular endothelial cells growth. I will highlight the mathematical mechanisms leading to the appearance of such patterns, and how some of these mechanisms can be observed in a 2x2 reduced coupled system of Ordinary Differential Equations (ODEs). I will also discuss how the model can help to characterize between healthy and diseased microscopic angiogenic patterns. I will provide theoretical results and numerical illustrations, on positivity of solutions for (1), the variety of patterns observed as a parameter varies, and bifurcation paths for the stationary solutions of the ODE which are relevant to understand the full PDE. Beyond these results, this article provides insights and perspectives on how to identify a few relevant parameters to characterize the diseased states and the underlying biochemical pathways. It also highlights a few new directions in a mathematical perspective. The biological observations were possible thanks to a collaboration with the Elahi Lab, a Neurology Lab at the Medical School at Mount Sinai in New-York. This talk relies on a joint work from 2024/2025 with A.F. Farroudji (Sorbonne Paris Nord), E. Stratigakou-Polychronaki and F.M. Elahi (Mount Sinai).
12:50 PM – 1:10 PM 116-A Short Communications

On the Periodic Homogenization of the Maxwell-Stefan Equations

We consider the periodic homogenization of the Maxwell-Stefan cross-diffusion system for three species with two equal binary diffusion coefficients. Via two-scale convergence, we derive the macroscopic limit and characterize the effective diffusion operator from cell problems. The limit equations describe diffusive transport of a gas mixture in a porous medium with periodic microstructure. To our knowledge, this constitutes the first rigorous homogenization result on the Maxwell-Stefan system. This work was carried out in collaboration with Claudia Nocita.
12:50 PM – 1:10 PM 115-B Short Communications

What Is Monogenity?

A number field $K$ is called monogenic if it has a power basis, i.e. there exists an algebraic integer $\alpha$ such that $\{1, \alpha, \cdots, \alpha^{n-1}\}$ is a basis of $K$ over $\mathbb{Q}$. Let $f(x)=x^{n}+ax^{3}+bx+c$ be the minimal polynomial of an algebraic integer $\theta$ over the field of rationals with certain conditions on $a,~b,~c,$ and $n.$ Let $K=\mathbb{Q}(\theta)$ be a number field and $\mathcal{O}_{K}$ be the ring of integers of $K.$ In this talk, we characterize all the prime divisors of the discriminant of $f(x)$ which do not divide the index of $\mathbb{Z}[\theta]$ in $\mathcal{O}_{K}.$ As an interesting corollary, we establish necessary and sufficient conditions for $\mathbb{Z}[\theta]$ to be integrally closed which implies the number field $K=\mathbb{Q}(\theta)$ is Monogenic. In addition, we investigate the types of solutions to certain differential equations associated with the polynomial $f(x)$ with the help of monogenity of the splitting field of $f(x)$.
1:10 PM – 1:30 PM 115-C Short Communications

Balancing Spectral Bias in Physics-Informed Neural Networks via Loss Design

We study the frequency bias of neural networks in function approximation and Physics-Informed Neural Networks (PINNs), highlighting how differential operators reshape spectral learning dynamics. Standard neural networks have a natural bias towards learning smooth, low-frequency functions, making it difficult for them to capture high-frequency details. For PINNs, this problem is exacerbated because the derivative operations in the PDE loss amplify errors in these high-frequency components, leading to an unbalanced training process that often fails on complex, multiscale problems. Motivated by this, we propose a new loss formulation that balances frequency components during training by weighting the loss function with Green’s function, a solution that intrinsically accounts for the physics and boundary conditions of the system. We compare its performance with standard PINNs on PDEs with multiscale features. Our results demonstrate that this new approach significantly improves the network’s ability to learn high-frequency features, leading to more accurate and robust solutions for complex physical systems.
1:10 PM – 1:30 PM 119-AB Short Communications

Classification of Subsets of Finite Fields of Characteristic 2 with Respect Its Closedness

The $r$-value of a subset in a finite additive group quantifies its degree of closedness. Subsets of $\mathbb{F}_{2^n}$ were categorised using these values and cardinality. Additionally, we use values found in $\mathbb{F}_{2^{n-1}}$ to list the $r$-values of $\mathbb{F}_{2^n}$. Schure triples and sum-free sets can be investigated using these values.
1:10 PM – 1:30 PM 118-AB Short Communications

Commutator of Calderón-Zygmund Operator in Fofana-Hardy Spaces

We prove that the commutator of a Calderón-Zygmund operator with an element in an appropriate subspace of BMO space is bounded in a Hardy-type space defined by taking, in the definition of classical Hardy spaces, the quasi-norm of Wiener amalgam spaces instead of the quasi-norm of Lebesgue spaces.
1:10 PM – 1:30 PM 118-C Short Communications

Complex Structures on Nilpotent Almost Abelian Lie Groups

The study of left-invariant geometric structures on nilpotent Lie groups is an active field of research and several results are known in low dimensions. A particularly intriguing problem within this field is the classification of nilpotent Lie groups that admit left-invariant complex structures. Although there are many contributions to the subject, it is considered a wild problem and in general it is far from being solved.  In this talk, we will focus on left-invariant complex structures on nilpotent almost abelian Lie groups. We will present the classification of nilpotent almost abelian Lie groups that admit left-invariant complex structures.These results were obtained through collaborative work with María Laura Barberis (Universidad Nacional de Córdoba & CONICET, Argentina), Verónica Díaz (Universidad Nacional de Mar del Plata, Argentina), Yamile Godoy (Universidad Nacional de Córdoba & CONICET, Argentina) and María Isabel Hernández (CONACYT - CIMAT Mérida, Mexico).
1:10 PM – 1:30 PM 120-AB Short Communications

Number Families Emerging from the Lengths of Bernstein-Based Words

The field of combinatorics on words, which is a new field of discrete mathematics, focuses on the study of formal languages, words and strings formed by letters or symbols. In this context, Kucukoglu and Simsek defined Bernstein-based words and investigated their properties by algebraic, combinatorial and algorithmic approaches in their recent paper [Construction of Bernstein-based words and their patterns, To appear in Math. Methods Appl. Sci., 2025]. In this presentation, Bernstein-based words and interesting number families emerging from their lengths will be handled. Moreover, some results on computational algorithms for generating special words and their colorful patterns will be presented. It will be also shown how the special words can be analyzed by aid of functions encoding their lengths to the coefficients of a formal power series. Eventually, this talk will end by a brief discussion on the generated special words and their potential applications in computational science and engineering.
1:10 PM – 1:30 PM 115-B Short Communications

Perfect Powers in Sequences of Polygonal Numbers

If $s$ is the number of sides in a regular polygon, the formula for the $n$-th $s$-gonalnumber is\[P_{s}(n) = \frac{(s-2)n^{2} - (s-4)n}{2}. \]If $s$ is the number of sides in a regular polygon, the formula for the $n$-th $s$-gonalnumber is\[P_{s}(n) = \frac{(s-2)n^{2} - (s-4)n}{2}. \]Consider the Diophantine equation \[P_{s}(n) = t^{m}\]for integers $n, s, t$ and $m > 2$. All solutions to this equation are known for $m>2$ and $s\in\{3,5,6,8,10,20\}$. Here we extend these results to the cases $s = 2k+4$ (where $k = 4,6$ or $5 \leq k \leq 97$ is a prime number) and $s = k+4$ (where $k = 9,15$ or $3 \leq k \leq 97$ is a prime number). The proofs of our results use the modular and hypergeometric methods, linear forms in logarithms and extensive calculations. We were unable to completely solve the above Diophantine equations, but we expect (based on GRH and weak effective abc conjecture) that there will be no additional solutions beyond those explicitly shown in our main results.This is a joint work with Andrzej Dabrowski, Salah Eddine Rihane and Paul Voutier.
1:10 PM – 1:30 PM 116-A Short Communications

Regularity of Velocity Averages in Kinetic Equations with Heterogeneity

We study regularity properties of kinetic equations with spatially heterogeneous coefficients. It is well known that, under suitable non-degeneracy assumptions, velocity averages of weak solutions exhibit compactness and improved regularity. While most existing results rely on spatially homogeneous transport fields, much less is known in the heterogeneous setting.In this talk, I present a new quantitative regularity estimate for velocity averages of weak solutions to kinetic equations with space-dependent drift terms. The result applies to weak solutions with low integrability and allows very general source terms. As a consequence, we obtain fractional regularity for averaged quantities in space and time. I will also discuss applications to heterogeneous conservation laws with discontinuous flux functions and to isentropic gas dynamics.This is joint work with Kenneth H. Karlsen (Oslo, Norway) and Darko Mitrović (Vienna, Austria).
1:10 PM – 1:30 PM 115-A Short Communications

The Fixed Point Property for (C)-Mappings and Unbounded Sets

In this talk, we will prove that a closed convex subset C of a real Hilbert space X has the fixed point property for (c)-mappings if and only if C is bounded. Some convergence results about the itérations are obtained.
1:30 PM – 1:50 PM 115-C Short Communications

Conformal Uncertainty, Categorically Explained

Conformal Prediction (CP) is a model-agnostic framework for distribution-free uncertainty quantification. Given (i) an exchangeable sample $y_1,\ldots,y_n \in Y$, (ii) a significance level $\alpha \in [0,1]$, and (iii) a function $\psi:Y^n \times Y \rightarrow \mathbb{R}$ that measures how well each observation conforms to the rest of the data, CP produces a Conformal Prediction Region (CPR) for $y_{n+1}$ with coverage at least $1-\alpha$. Despite its recent prominence in statistics and machine learning research, the mathematical nature of the uncertainty represented by CPRs remains opaque: CP regions are ordinal indicators of uncertainty (larger regions indicate higher uncertainty), yet lack a cardinal interpretation (twice as large regions do not imply twice the uncertainty).{\bf Contributions.} We provide a category-theoretic characterization of CP that reveals its latent cardinal uncertainty quantification capabilities.1. We introduce two categories$\bullet$ $\mathbf{UHCont}$, whose objects are topological spaces and morphisms are upper hemicontinuous set-valued functions (also called correspondences); and$\bullet$ $\mathbf{{WMeas}_\text{uc}}$, whose objects are compact Polish spaces and morphisms are weakly measurable, uniformly compact-valued correspondences.The CP method defines a morphism in both categories. 2. {\bf Theorem (informal).} If $Y$ is compact Hausdorff, $\psi$ is jointly continuous on $Y^n \times Y$ and invariant to permutations in $Y^n$, and $\alpha$ does not hit the discrete split-conformal levels, then deriving a CPR is equivalent to first obtaining a set $\mathcal{M}$ of probability measures on $Y$, and then extracting from $\mathcal{M}$ an Imprecise Highest-Density Region (IHDR)---a set-valued analogue of classical confidence intervals. Equivalence here is formalized by a commuting diagram in $\mathbf{UHCont}$ and $\mathbf{{WMeas}_\text{uc}}$.The set $\mathcal{M}$ is used to cardinally quantify uncertainty, e.g. via the generalized Hartley measure. We provide an example where $Y=[0,1]^d$ represents the space of images. 3. As a byproduct, CP is shown to bridge Bayesian, frequentist, and imprecise-probabilistic paradigms: under standard posterior predictive consistency assumptions, a diagram linking the CPR, the posterior predictive $\alpha$-level set, and the IHDR commutes asymptotically.This formulation situates CP within a unified categorical framework for uncertainty. arXiv:2507.04441
1:30 PM – 1:50 PM 115-B Short Communications

Existence of Simple Non-Cyclic Abelian Varieties Over Arbitrary Finite Fields and of a Given Dimension g>1

Vladuts characterized in 1999 the set of finite fields $k$ such that all elliptic curves defined over $k$ have a cyclic group of rational points. Under the conjecture of infinitely many Mersenne primes, this set is infinite. In these notes we prove that there is no a finite field $k$ such that all the simple abelian varieties defined over $k$ of dimension $g>1$ have a cyclic group of rational points.
1:30 PM – 1:50 PM 115-A Short Communications

Fundamental n-quandles of Links Are Residually Finite

We present some recent results on the residual finiteness and subquandle separability of quandles, properties that respectively imply the solvability of the word problem and the generalized word problem for these non-associative structures. Fundamental $n$-quandles of oriented links are canonical quotients of their fundamental quandles, and are closely related to $n$-fold cyclic branched covers of the 3-sphere branched over links. We prove that the fundamental $n$-quandle of any oriented link in the 3- sphere is residually finite for each $n \ge 2$. This supplements the recent result on residual finiteness of fundamental quandles of oriented links, as well as the classification of links whose fundamental $n$-quandles are finite for some $n$.
1:30 PM – 1:50 PM 118-C Short Communications

Gromov–Lawson and Gromov Conjectures for Kähler Metrics

The conjectures of Gromov–Lawson and Gromov predict obstructions to the existence of Riemannian metrics of positive scalar curvature on closed manifolds in terms of their asphericity and large-scale geometry, respectively. In this talk, I will address these conjectures for Kähler metrics on smooth projective varieties. In detail, I will show that a smooth projective variety that is aspherical (or, more generally, whose universal cover has maximum macroscopic dimension) cannot support a Kähler metric of positive scalar curvature. The statement will be refined for totally non-spin manifolds and complex projective surfaces. The proofs of these results draw new connections between the theories of minimal models, positivity in complex algebraic geometry, and macroscopic dimensions. This talk is based on joint work with Luca F. Di Cerbo and Alexander Dranishnikov.

1:30 PM – 1:50 PM 116-A Short Communications

Nonlocal Gradients, Nonlocal Sobolev Spaces, and Variational Problems

In this talk, we present recent progress on the theory of nonlocal gradients—of which the Rieszfractional gradient is a paradigmatic example—and the associated nonlocal Sobolev spaces. Inparticular, we provide characterizations of nonlocal gradients for which the corresponding non-local Sobolev-type functional spaces exhibit desirable structural properties, such as continuousand compact embeddings into Lebesgue or Orlicz spaces. We also discuss applications to newnonlocal PDEs and variational principles based on nonlocal gradients.
1:30 PM – 1:50 PM 119-AB Short Communications

On Families of Graphs with Constant Modular Irregularity Strength

Let $G=(V,E)$ be a finite and connected graph with order $n$. An edge $k$-labeling $\phi : E \to \{1,2,\dots,k\}$ is called modular irregular labeling of a graph $G$ if the weight function, $\sigma:V(G) \to \mathbb{Z}_n$, defined by a bijective $\sigma(u) = wt_\phi (u) = \sum_{uv \in E(G)}\phi(uv)\pmod{n}$ with $\mathbb{Z}_n$ is the group of integers modulo $n$. The function $\sigma(u)$ is called a modular weight of the vertex $u$. The modular irregularity strength of a graph $G$ is a minimum number $k$ such that the graph $G$ has a modular irregular labeling. In this talk, we discuss several classes of graphs that have constant modular irregularity strength. Specifically, a family of graph that can be modified from complete graphs and multipartite graphs.\\ {\bf Keywords:} modular irregularity strength; modular irregular labeling. complete graph, complete multipartite.\\
3:00 PM – 3:45 PM 118-C Section Lecture

3-D Anisotropic vs Classical Incompressible Navier-Stokes Equations

In this article, we begin by reviewing some classical results on the existence and regularity theory of the three-dimensional incompressible Navier--Stokes system (denoted by (NS)). We then present our results on the global well-posedness of the three-dimensional anisotropic Navier--Stokes system ((ANS)), which has dissipation only in the x_1 and x_2 directions. In the third part of this article, we establish regularity criteria and well-posedness results for the system (NS). We emphasize that the proofs of these results rely essentially on the anisotropic analysis developed in our study of (ANS). Finally, we present our results on lower bound estimates for the analyticity radius of solutions to both (NS) and (ANS).
3:00 PM – 3:45 PM 121-AB Section Lecture

Constructing Fibrations in 4D

I will discuss the relationship between fibered knots in the 3-sphere (a classic 3D topic) and some major open problems in 4-dimensional topology. These motivate us to study an analogue of fibered knots in the 4-ball and 4-sphere. I will show some constructive techniques that work in this dimension and demonstrate some interesting examples of fibered surface links.
3:00 PM – 3:45 PM 118-AB Section Lecture

Control of Some Coupled Pde Systems of Mixed Types

The initial part of the talk reviews some results on control and stabilization of some coupled PDE systems of mixed types, obtained with our collaborators. The latter part is specifically on new results with our collaborators, on stabilization or the lack of, for these systems. An outline of the proof for both positive and negative results will be indicated. These do not use the full knowledge of the spectrum. The negative result relies on a construction of highly localized solutions using certain ansatz involving complex exponentials and hence works for such coupled systems with variable coefficients and lower order terms.
3:00 PM – 3:45 PM 119-AB Section Lecture

Recent progress in graph theory using expansion

Graph expansion has long been recognised as an important and desirable property with applications in a wide range of areas in computer science and mathematics. A form of expansion known as `sublinear expansion' has been used particularly successfully in the last decade in extremal graph theory, playing a pivotal role in the progress on, and resolution of, a range of long-standing and notable problems. This talk will cover some of these advances, highlighting the role of sublinear expansion and the settings in which it is effective.

3:00 PM – 3:45 PM 115-A Section Lecture

Reduction from Representations of p-adic Groups to Representations of Finite Groups

Representations of p-adic groups, e.g., invertible matrices over the p-adic numbers, are an intensely studied area of mathematics that also plays a key role in the Langlands program and has applications to automorphic forms (generalizations of modular forms), among others. In my talk I will explain what I mean by p-adic groups and then I might survey the current state of the art of our understanding of the structure of the whole category of representations of p-adic groups, including recent and forthcoming results that relate the blocks of this category to depth-zero blocks of another p-adic group under minor tameness assumptions. Depth-zero representations correspond to representations of finite groups of Lie type and are much better understood than general representations of p-adic groups. Relating arbitrary blocks to depth-zero blocks therefore allows us to reduce many problems about representations of p-adic groups and the Langlands program to depth-zero representations, where the answer is either already known or easier to achieve.This reduction-to-depth-zero result has recently been obtained for representations with complex coefficients in two joint preprints with Jeffrey Alder, Manish Mishra and Kazuma Ohara. The case of representations with much more general coefficient rings is joint work in progress with Jean-François Dat. The techniques used in both cases are quite different, as I might sketch in my talk.
3:00 PM – 3:45 PM 122-AB Section Lecture

Rigidity in Complex Dynamics: Multiplier Spectrum and Dynamical André-Oort Conjecture

In this lecture, we present recent progress on rigidity problems in one-dimensional complex dynamics, including the proof of Dynamical André-Oort conjecture for curves and generic injectivity of multiplier spectrum. The proofs combine ideas from algebraic geometry, Arakelov geometry and complex dynamics.
3:00 PM – 3:45 PM 120-AB

The Geometry of Spherical Spin Glasses

Consider a centered Gaussian field $H_N$ on the unit sphere in the Euclidean space of dimension $N$. Suppose it is stationary, so that we can write its covariance function as $f(x\cdot y)/N$ for some $f$. With the function $f$ fixed, how does the volume of a level set of $H_N$ at height $E$ scale as $N\to\infty$? What can be said about the geometry of this set? In the language of statistical physics, the former question is equivalent to computing the free energy of the spherical spin glass model, while the latter is closely related to understanding the structure of its Gibbs measure.

In 1980, Parisi's celebrated (highly non-rigorous) replica symmetry breaking solution gave an answer to these questions. Decades later, his formula for the free energy was proved by Talagrand, while his conjecture on ultrametricity of the Gibbs measure was resolved by Panchenko. Together with other developments, these results provide a complete asymptotic description of the Gibbs measure, but only up to rotations and without directly identifying the corresponding regions of the energy landscape defined by $H_N$. 

In this talk I will describe two related characterizations of the regions on which the Gibbs measure concentrates, identifying them as "bands" around approximate maximizers of $H_N$ at different radii. First, I will briefly discuss a precise analysis of the Gibbs measure and free energy for the pure models, based on a detailed study of critical points and their neighborhoods. I will then describe another, more general, method based primarily on first principles in combination with concentration estimates. Despite its relatively elementary ingredients, this technique leads to a rigorous proof and extension of several predictions from the well-known Thouless-Anderson-Palmer approach and connects it to the Parisi solution in a natural way. Finally, I will mention how these geometric results led to an optimization algorithm that is provably optimal within a natural class of stable algorithms.

3:00 PM – 3:45 PM 116-A Section Lecture

The Subspace Flatness Conjecture

The covering radius $\mu(\Lambda,K)$ of a convex body $K \subseteq \setR^n$ with respect to a full rank lattice $\Lambda \subseteq \setR^n$ is the minimum scaling needed so that translates of $K$ placed at every lattice point cover the whole $\setR^n$. A question going back to work of Kannan and Lov\'asz (1988) is how well the covering radius is described solely by the volume of $K$ and the density of the lattice, after projecting both into a suitable subspace.
 We report on significant progress on this question due to Regev and Stephens-Davidowitz (2016) who resolve this problem for ellipsoids and Reis and Rothvoss (2023) who cover the general case.
 We also survey applications of these results that give near-optimal bounds on the flatness constant as well as a $(\log n)^{O(n)}$-time algorithm for solving $n$-variable integer programs, following work of Dadush (2012).
 This is based on joint work with Victor Reis.

3:30 PM – 4:30 PM Terrace Ballroom Public Lecture

Magic Squares, Cubes, and Hypercubes: From Ancient Origins to Recent Advances

Inscribed on a wall near the entrance of the majestic Parshvanath Jain Temple in Khajuraho, India (built around 960 CE) is a 4 × 4 magic square with remarkable arithmetic properties. We will explain why this magic square is the unique one of its kind, up to certain transformations.  This answers a question posed by the legendary geometer HSM Coxeter in 1938.  We will also explain why there is a unique such magic object in every dimension.

 

4:00 PM – 4:45 PM 118-AB Section Lecture

Computing Multiple Solutions of Systems of Nonlinear Equations with Deflation

Many systems of nonlinear equations admit multiple solutions, which are often crucial for understanding the problem at hand. Algorithms for computing multiple solutions have been developed over several decades in the context of numerical bifurcation analysis, with great success. However, the core algorithms of continuation, bifurcation detection, and branch switching can miss branches of solutions not connected to the given initial solution. They can also be complex to apply to large-scale discretisations of the nonlinear partial differential equations that arise in many real-world problems. A complementary alternative is to employ deflation, which modifies the nonlinear problem so that the Newton--Kantorovich iteration cannot rediscover known solutions, and thus if the iteration converges it finds a new solution. Deflation enables the discovery of disconnected branches. Moreover, when combined with natural or tangent continuation, the resulting subproblems can be efficiently solved if a good preconditioner is available for the original Newton step, making the method convenient and practical to apply at large scale. In this talk we introduce deflation, discuss how it may be combined with classical approaches to yield effective algorithms for discovering multiple solutions of partial differential equations and variational inequalities, and outline some open problems.
4:00 PM – 4:45 PM 115-A Section Lecture

Higher Property T, Banach Representations and Applications

Property T is a group property that could be phrased by means of cohomological vanishing in degree 1 and unitary coefficients. Higher property T is the higher degree analogue. It is related to various analytic, topological and geometrical rigidity phenomena. Prominent examples of groups with higher property T are lattices in simple Lie groups. Recently, several open conjectures were proven using higher property T and some of its variants. I will survey the topic, following my joint work with Roman Sauer and my joint work with Saar Bader, Shaked Bader and Roman Sauer.

4:00 PM – 4:45 PM 121-AB Special Section Lecture

Lagrangian Floer Theory, from Geometry to Algebra and Back Again

We survey various aspects of Floer theory and its place in modern symplectic geometry, from its introduction to address classical conjectures of Arnold about Hamiltonian diffeomorphisms and Lagrangian submanifolds, to the rich algebraic structures captured by the Fukaya category, and finally to the idea, motivated by mirror symmetry, of a "geometry of Floer theory" centered around family Floer cohomology and local-to-global principles for Fukaya categories.
4:00 PM – 5:00 PM Hall E - Expo Poster Presentations

Poster Exhibition

"Collapsing of Minimality Conditions in Divisible Ordered Abelian Groups" by Jacob Stern (1 - Logic)

"Gotzmann thresholds of monomials: a general method and its application" by Vittoria Bonanzinga (2 - Algebra)

"On a Finite-Iteration Method for Solving SLAE" by Roman Filippov (2 - Algebra)

"Nilpotent associative algebras" by Ikboljon Karimjanov (2 - Algebra)

"Sets of lengths of integer-valued polynomials on prime ideals" by Sarah Nakato (2 - Algebra)

"On Complete Integral Closedness, Skew-Injectivity, and π-Injectivity of Modules" by Muamar Musa Nurwigantara (2 - Algebra)

"Representations and Cohomologies of the Alternating Group of Degree 4" by Andriiana Plakosh (2 - Algebra)

"Enumerating Log Rational Curves on $\mathbb{P}_{\mathbb{P}^r}(\mathcal{O}^s\oplus \mathcal{O}(-a))$" by Naufil Sakran (2 - Algebra)

"Weitzenböck Remainder Spectrum on Rational Omogeneous Varieties" by Lucas Almeida (5 - Geometry)

"Study of Clairaut Anti-Invariant Riemannian Maps from Sasakian Manifolds" by Garima Goel (5 - Geometry)

"Sharp Minkowski Type Inequality in Cartan-Hadamard 3-Spaces" by Fang Hong (5 - Geometry)

"A Study of Lightlike Submanifolds of Indefinite Statistical Manifolds" by Varun Jain (5 - Geometry)

"Compact Holonomy and Riemannian Metrizability in Finsler Geometry" by Sendrasoa Laurence Lantonirina (5 - Geometry)

"Infinitesimal Bending of Dual Curves and Its Geometric Characterizations" by Marija Najdanović (5 - Geometry)

"Quadratic Killing tensors on Symmetric Spaces" by An Ky Duy Nguyen (5 - Geometry)

"On the dimension of the nullity space of the curvature tensor on Riemannian manifold" by Princy Randriambololondrantomalala (5 - Geometry)

"Study of Holomorphic Riemannian Maps from Nearly Kaehler Manifolds" by Rashmi Sachdeva (5 - Geometry)

"On the Roter type of Generalised Wintgen Ideal Legendrian Submanifolds" by Aleksandar Šebeković (5 - Geometry)

"GEOMETRY OF POINT PARTICLES. SYMBOLIC COMPUTER VERIFICATION OF THE ATIYAH’S CONJECTURE FOR FIVE POINTS IN THE EUCLIDEAN PLANE" by Dragutin Svrtan (5 - Geometry)

"Bonnet--Myers-type Theorems via Bakry--\'{E}mery Ricci Curvature of Exponential Decays" by Homare Tadano (5 - Geometry)

"Area-minimizing capillary cones" by Raphael Tsiamis (5 - Geometry)

"On Shape and Energies of Geometric Objects " by Ljubica Velimirovic (5 - Geometry)

"Graph Manifolds with Positive Artinian Presentations" by Lorena Armas-Sanabria (6 - Topology)

"The Chordal Distance Tr+[@[Abstract Title - Plain Text]]sform of Geometric Loops and its Persistent Homology" by James Binnie (6 - Topology)

"On Projective and Flat Persistence Modules" by Giriraj Ghosh (6 - Topology)

"Corank-One Orthosymplectic Reduction Superalgebras" by Marcus McLaurin (7 - Lie Theory and Generalizations)

4:00 PM – 5:00 PM Hall E - Expo Poster Presentations

Poster Presentation by Author

"Collapsing of Minimality Conditions in Divisible Ordered Abelian Groups" by Jacob Stern (1 - Logic)

"Gotzmann thresholds of monomials: a general method and its application" by Vittoria Bonanzinga (2 - Algebra)

"On a Finite-Iteration Method for Solving SLAE" by Roman Filippov (2 - Algebra)

"Nilpotent associative algebras" by Ikboljon Karimjanov (2 - Algebra)

"Sets of lengths of integer-valued polynomials on prime ideals" by Sarah Nakato (2 - Algebra)

"On Complete Integral Closedness, Skew-Injectivity, and π-Injectivity of Modules" by Muamar Musa Nurwigantara (2 - Algebra)

"Representations and Cohomologies of the Alternating Group of Degree 4" by Andriiana Plakosh (2 - Algebra)

"Enumerating Log Rational Curves on $\mathbb{P}_{\mathbb{P}^r}(\mathcal{O}^s\oplus \mathcal{O}(-a))$" by Naufil Sakran (2 - Algebra)

"Weitzenböck Remainder Spectrum on Rational Omogeneous Varieties" by Lucas Almeida (5 - Geometry)

"Study of Clairaut Anti-Invariant Riemannian Maps from Sasakian Manifolds" by Garima Goel (5 - Geometry)

"Sharp Minkowski Type Inequality in Cartan-Hadamard 3-Spaces" by Fang Hong (5 - Geometry)

"A Study of Lightlike Submanifolds of Indefinite Statistical Manifolds" by Varun Jain (5 - Geometry)

"Compact Holonomy and Riemannian Metrizability in Finsler Geometry" by Sendrasoa Laurence Lantonirina (5 - Geometry)

"Infinitesimal Bending of Dual Curves and Its Geometric Characterizations" by Marija Najdanović (5 - Geometry)

"Quadratic Killing tensors on Symmetric Spaces" by An Ky Duy Nguyen (5 - Geometry)

"On the dimension of the nullity space of the curvature tensor on Riemannian manifold" by Princy Randriambololondrantomalala (5 - Geometry)

"Study of Holomorphic Riemannian Maps from Nearly Kaehler Manifolds" by Rashmi Sachdeva (5 - Geometry)

"On the Roter type of Generalised Wintgen Ideal Legendrian Submanifolds" by Aleksandar Šebeković (5 - Geometry)

"GEOMETRY OF POINT PARTICLES. SYMBOLIC COMPUTER VERIFICATION OF THE ATIYAH’S CONJECTURE FOR FIVE POINTS IN THE EUCLIDEAN PLANE" by Dragutin Svrtan (5 - Geometry)

"Bonnet--Myers-type Theorems via Bakry--\'{E}mery Ricci Curvature of Exponential Decays" by Homare Tadano (5 - Geometry)

"Area-minimizing capillary cones" by Raphael Tsiamis (5 - Geometry)

"On Shape and Energies of Geometric Objects " by Ljubica Velimirovic (5 - Geometry)

"Graph Manifolds with Positive Artinian Presentations" by Lorena Armas-Sanabria (6 - Topology)

"The Chordal Distance Tr+[@[Abstract Title - Plain Text]]sform of Geometric Loops and its Persistent Homology" by James Binnie (6 - Topology)

"On Projective and Flat Persistence Modules" by Giriraj Ghosh (6 - Topology)

"Corank-One Orthosymplectic Reduction Superalgebras" by Marcus McLaurin (7 - Lie Theory and Generalizations)

4:00 PM – 4:45 PM 120-AB Section Lecture

Spin Glasses and the Parisi Formula

Spin glasses are models of statistical mechanics in which a large number of simple elements interact with one another in a disordered fashion. One of the fundamental results of the theory is the Parisi formula, which identifies the limit of the free energy of a large class of such models. Yet many interesting models remain out of reach of the classical theory, and direct generalizations of the Parisi formula yield invalid predictions. I will report on some partial progress towards the resolution of this problem, which also brings a new perspective on classical results.
4:00 PM – 4:45 PM 118-C Section Lecture

Stable Solutions to Reaction-Diffusion Elliptic Problems

The talk will concern stable solutions to reaction-diffusion elliptic PDEs. We will begin with regularity questions, first addressing the classical Laplacian. In joint work with Figalli, Ros-Oton, and Serra, we proved that stable solutions are smooth up to the optimal dimension 9, thereby solving an open problem posed by Brezis in the mid-1990s. I will describe this result and also discuss related progress and open problems for the fractional Laplacian -arising naturally in boundary reaction problems-, the p-Laplacian, and minimal surfaces.We will then turn to existence questions, starting with the Casten-Holland and Matano theorem for interior reactions, which states that no nonconstant stable solution exists in convex domains under zero Neumann boundary conditions. I will present a recent result with Cónsul and Kurzke establishing that the analogous statement fails for boundary reactions. This requires the development of a new Ginzburg-Landau theory for real-valued functions and the analysis of the half-Laplacian on the real line, for which I will present new results and open problems.
4:00 PM – 4:45 PM 119-AB Section Lecture

The Combinatorial Geometry of Particle Physics

Recent breakthroughs in the study of scattering amplitudes have uncovered profound and unexpected connections with combinatorial geometry. These connections range from classical structures -- such as polytopes, matroids, and Grassmannians -- to more modern developments including positroid varieties and the amplituhedron. Together they point toward the unifying framework of positive geometry, in which geometric domains canonically determine analytic functions governing scattering processes. This talk traces the emergence of positive geometry from the physics of amplitudes.
4:00 PM – 4:45 PM 116-A Section Lecture

The Mean-Field Dynamics of Transformers

We develop a mathematical framework that interprets Transformer attention as an interacting particle system and studies its continuum (mean-field) limits. By idealizing attention on the sphere, we connect Transformer dynamics to Wasserstein gradient flows, synchronization models (Kuramoto), and mean-shift clustering. Central to our results is a global clustering phenomenon whereby tokens cluster asymptotically after long metastable states where they are arranged into multiple clusters. We further analyze a tractable equiangular reduction to obtain exact clustering rates, show how commonly used normalization schemes alter contraction speeds, and identify a phase transition for long-context attention. The results highlight both the mechanisms that drive representation collapse and the regimes that preserve expressive, multi-cluster structure in deep attention architectures.
4:00 PM – 4:45 PM 122-AB Section Lecture

Toward Criteria for the K-Stability of Fano Manifolds

4:30 PM – 5:30 PM Benjamin Franklin Stage Films @ ICM

Math Circles Around the World & Math Camp 1729 (Double Feature)

Film Directed by Ekaterina Eremenko

Every week, hundreds of children in different cities of the world meet to solve complex problems. Who they are, why they do it and how, in the movie “Mathematical Circles Around the World”.

Source: Discretization in Geometry and Dynamics

5:00 PM – 5:45 PM 119-AB Section Lecture

Chaos on Surfaces and Beyond

We present some developments in the study of chaotic dynamics following the solution of a conjecture of Newhouse on the measures maximizing the entropy of smooth surface diffeomorphisms. We focus on strong positive recurrence, a generalization of the classical Anosov-Smale theory of uniform hyperbolicity which we introduced with Sylvain Crovisier and Omri Sarig. We will explain why this new property is general enough to be satisfied by all smooth surface diffeomorphisms with positive entropy. Then we will see how many quantitative properties such as exponential mixing or limit theorems for regular functions follow from it. We also present some open problems, including its abundance (or not) in higher dimensions.
5:00 PM – 5:45 PM 121-AB Section Lecture

Minimal Surfaces of Finite Genus: Classification, Dynamics and Laminations

We will revise a program to study complete and properly embedded minimal surfaces in Euclidean three-space \(\mathbb{R}^3\), developed jointly with W.H. Meeks and A. Ros in the last three decades. After recalling the role of the classical Riemann minimal examples in minimal surface theory, we explain our four-step classification of properly embedded minimal surfaces of genus zero and infinite topology in \(\mathbb{R}^3\): the periodic case, the quasi-periodicity of the two-limit-ended case, the non-existence of one-limit-ended examples, and the final classification. We then review the lamination techniques (limit-leaf stability, local removable singularity, and singular structure theorems), the dynamics theorem, bounds on topology and index for complete embedded minimal surfaces of finite total curvature, and the resolution of the embedded Calabi-Yau problem for finite genus and countably many ends. Throughout we emphasize the interaction between topology, flux, curvature estimates, and the structure of related moduli spaces.
5:00 PM – 5:45 PM 120-AB Section Lecture

New and Old Mathematical Results on Wave Turbulence Theory

In this lecture we give an overview of some recent mathematical advances in wave turbulence theory. We start with the original perspective of Bourgain on the study of the energy spectrum for a periodic nonlinear Schrödinger equation. Then we introduce wave kinetic equations as effective equations for the energy spectrum derived from weakly nonlinear dispersive equations and we end with examples of rigorous proofs of condensate growth and energy transfer.
5:00 PM – 5:45 PM 118-AB Section Lecture

Nonlinear Least-Squares Finite Element Methods for the Monge-Ampere Equations

We present finite element methods that can capture smooth convex solutions of Monge-Ampere equations. They are formulated as nonlinear least-squares problems on novel finite element spaces whose degrees of freedom can be used to enforce the local convexity of the finite element solutions.
5:00 PM – 5:45 PM 116-A Section Lecture

Nonparametric Inference Under Shape Constraints: Past, Present and Future

Traditionally, we think of statistical methods as being divided into parametric approaches, which can be restrictive, but where estimation is typically straightforward (e.g.~using maximum likelihood), and nonparametric methods, which are more flexible but often require careful choices of tuning parameters. Nonparametric inference under shape constraints sits somewhere in the middle, seeking in some ways the best of both worlds. I will provide a historical overview of the field, as well as a perspective on its current state, concluding with some thoughts on future directions and open problems.
5:00 PM – 5:45 PM 115-A Section Lecture

On Geometric Models in Representation Theory

Geometric models have emerged as an important tool in the representation theory of algebras. Surface models associated to gentle algebras have been particularly fruitful in advancing our understanding of their module and derived categories. We give an overview of some of the theoretical advances that geometric surface models for the derived categories of graded gentle algebras and their connections to Fukaya categories of surfaces have made possible.
5:00 PM – 6:30 PM Terrace Ballroom Roundtable / Panel

Panel: AI in College Math Education

Rapid advances in AI are providing challenges and opportunities in undergraduate mathematics education, for both teachers and learners.  We will attempt to give some perspective on a quickly-changing landscape:  disruptions in traditional assessment; new frontiers in personalized learning; experiments in pedagogy; and more.

Moderator: Ravi Vakil, Stanford University

Panelists:  

  • Jarod Alper, University of Washington
  • Emily Braley
  • Alex Kontorovich, Rutgers University 
  • Barbara Oakley, Oakland University

 

5:00 PM – 5:45 PM 118-C Section Lecture

The Boundaries of Von Neumann Algebras

The theory of von Neumann algebras was initially developed in the 1930s by Murray and von Neumann, providing a far reaching generalization of classical measure theory. Von Neumann algebras themselves were therefore initially studied as inherently analytic objects. This perspective was reinforced, and then almost immediately afterword dismantled, by Alain Connes starting in the 1970s when he showed that there is a unique separable injective II1 factor, and then also provided the first example of rigidity phenomena in von Neumann algebras through the use of Kazhdan's property (T). The juxtaposition of these two extremes led Popa's breakthrough in establishing deformation/rigidity theory, leading to numerous other breakthroughs and a deeper understanding of structural theory of von Neumann algebras. Von Neumann algebras therefore have a rich structure and it is only by studying the field from many different perspectives that we can gain a clearer picture of these mysterious objects. Each of the perspectives from ergodic theory, Voiculescu's free probability theory, abstract harmonic analysis, and other contribute to our understanding of the area. We describe a new perspective stemming from the dynamics of boundary actions. This has its origins in the work of Ozawa on applications of amenable actions, but it has only recently been realized that these boundaries are inherent to the von Neumann algebras themselves. These boundaries allow for the incorporation of geometric boundary techniques in the von Neumann algebraic setting. We survey some properties described using these boundaries as well as some rigidity results obtained using these techniques.
5:00 PM – 5:45 PM 122-AB Section Lecture

The Orbit Method, Microlocal Analysis and Applications to L-Functions

L-functions are generalizations of the Riemann zeta function.  Their analytic properties control the asymptotic behavior of prime numbers in various refined senses. Conjecturally, every L-function is a "standard L-function" arising from an automorphic form. A problem of recurring interest, with widespread applications, has been to establish nontrivial bounds for L-functions.  I will survey some recent results addressing this problem. The proofs involve the analysis of integrals of automorphic forms, approached through the lens of representation theory.  I will emphasize the role played by the orbit method, developed in a quantitative form along the lines of microlocal analysis, as well as inputs from the theory of homogeneous dynamics and effective equidistribution.

6:00 PM – 6:45 PM 118-AB Section Lecture

Acceleration Techniques at the Interface of Optimization, Linear Algebra, and Machine Learning

The talk will begin with the classical gradient descent algorithm for convex optimization. An interesting property of its iterates is that , asymptotically, they tend to oscillate within a two-dimensional subspace. By exploiting structural knowledge of the gradients - specifically, that they effectively correspond to iterates of a shifted power method - it is possible to significantly accelerate the algorithm. This idea is further developed through the use of a projection step based on the Lanczos algorithm.When the step size in gradient descent is held constant, the algorithm reduces to a fixed-point iteration, which naturally raises the question of how such iterations can be accelerated efficiently. Acceleration techniques for fixed-point iterations have evolved along several distinct directions. On one hand, Krylov subspace methods adopted a projection-based approach, similar to the one discussed earlier. On the other hand, extrapolation perspectives have also been developed, including methods such as Reduced Rank Extrapolation [Mesina, 1977; Eddy, 1979] and the closely related Anderson acceleration [1965]. In addition, Quasi-Newton and Inexact Newton methods may also be interpreted as acceleration strategies, as they too seek fixed points of iterative schemes using essentially the same building blocks as fixed-point accelerators. Thus, acceleration methods have emerged from multiple perspectives and were often developed independently despite being founded on identical core principles.A timely question is whether or not these methods can be extended to accelerate stochastic sequences of the kind commonly encountered in machine learning. As will be illustrated, this question does not have a simple answer, since acceleration and extrapolation techniques fundamentally rely on smoothness, whereas stochastic sequences are inherently noisy by design.The presentation will provide a brief survey of acceleration techniques while aiming to place these methods in a modern context, highlighting their relevance and applications in machine learning.
6:00 PM – 6:45 PM 115-A Special Section Lecture

Oligomorphic Groups and Tensor Categories

A pre-Tannakian category is a kind of tensor category modeled on representation categories of algebraic groups. Despite being an important and natural class of objects, they are still poorly understood, in large part due to the dearth of examples. In recent work with Harman, we introduced a new construction of tensor categories based on oligomorphic groups, a class of permutation groups arising in model theory. Our construction has led to a number of new examples of pre-Tannakian categories that are fundamentally different from those previously known. I will give an overview of our work and some subsequent developments.
6:00 PM – 6:45 PM 120-AB Section Lecture

Probabilistic and Statistical Mechanics Approaches to The Box-Ball System and Related Discrete Integrable Systems

The box-ball system (BBS), introduced as a soliton cellular automaton, exhibits deep connections with classical integrable systems such as the discrete and ultra-discrete KdV equations and the Toda lattice. While these systems have been extensively studied from deterministic and algebraic perspectives, probabilistic and statistical mechanics approaches have been rapidly developing in recent years, particularly in the infinite-volume setting.In this talk, I will provide an overview of these advances, focusing on the rigorous construction of infinite systems and the analysis of stationary distributions across several integrable models. Special attention will be given to the BBS, where significant progress has been made in two directions: (1) understanding the macroscopic dynamics of tagged solitons, including their convergence to Brownian motion under suitable scaling, and (2) establishing a rigorous generalized hydrodynamic limit—a hydrodynamic theory developed for integrable systems with infinitely many conserved quantities.A key theme throughout the talk will be the role of structures such as the Pitman transform and the independence preserving property, which offer a unifying probabilistic framework across different models. I will also discuss ongoing challenges and outline open problems at the intersection of probability theory, integrable systems, and mathematical physics.
6:00 PM – 6:45 PM 122-AB Section Lecture

Reasonable Bounds in the Polynomial Szemerédi Theorem

In 1975, Szemerédi proved that any subset of the natural numbers with positive upper density must contain arbitrarily long finite arithmetic progressions. This result has since been generalized to guarantee the existence of a wide variety of arithmetic configurations in dense subsets of the integers. Gowers gave the first proof of reasonable quantitative bounds in Szemerédi's theorem in 2001, and posed the problem of doing the same in the polynomial Szemerédi theorem of Bergelson and Leibman. A significant amount of progress has been made on this problem in the last few years. We will survey these developments, present some of the key new ideas behind their proofs, and describe further applications.
6:00 PM – 6:45 PM 121-AB Section Lecture

Strong Closing Lemmas in Hamiltonian Dynamics

I will talk about strong closing lemmas in Hamiltonian dynamics that are proved using spectral invariants (also known as action selectors) in symplectic geometry. I will review strong closing lemmas in low-dimensional Hamiltonian dynamics (Reeb flows on contact three-manifolds and area-preserving maps on symplectic surfaces) and outline the key ideas behind their proofs. I will also discuss results concerning strong closing lemmas in high-dimensional Hamiltonian dynamics, as well as analogous results for minimal hypersurfaces.
6:00 PM – 6:45 PM 118-C Section Lecture

The Circle Method and Pointwise Ergodic Theorems

The purpose of this lecture is to discuss the circle method and its quantitative role in understanding pointwise almost everywhere convergence phenomena for polynomial ergodic averaging operators. Specifically, we will use the circle method to illustrate that pointwise almost everywhere convergence and norm convergence in ergodic theory can have fundamentally different natures. More importantly, these differences may necessitate the use of distinct types of tools, which can sometimes be more intriguing than the original problems themselves.
6:00 PM – 6:45 PM 116-A Section Lecture

The Role of Algorithmic Stability in Distribution-Free Inference

In statistics and machine learning, an algorithm that inputs training data and returns a fitted model is said to satisfy algorithmic stability if its output is not substantially altered by randomly resampling or removing a small number of data points from the training set. Algorithmic stability plays a crucial role in many results in statistics, particularly in the assumption-lean or distribution-free regime where we aim to avoid placing assumptions on the distribution of the data. At the same time, we may also want to certify that an algorithm is stable, or to construct an algorithm that is guaranteed to be stable, again in a distribution-free way if possible. This talk will highlight some results that span these different questions. Specifically, we will see how algorithmic stability allows for cross-validation to be used for distribution-free predictive inference. However, we will also see an impossibility result that limits our ability to certify that a black-box algorithm is stable without making assumptions. Fortunately, by using bagging (averaging over models fitted to repeated subsamples of the data), any black-box algorithm can be automatically guaranteed to be stable. In combination, these findings illustrate some of the benefits and challenges of the algorithmic stability framework in the distribution-free regime. The results presented in this talk are based on joint work with Emmanuel Candes, Aaditya Ramdas, Ryan Tibshirani, Jake Soloff, Rebecca Willett, Byol Kim, and Yuetian Luo.
6:00 PM – 6:45 PM 119-AB Section Lecture

Wild Dynamics on Manifolds

We survey a few results on differentiable, symplectic, or analytic wild dynamics.
6:30 PM – 9:30 PM Receptions & Special Events

Emmy Noether Talk at Bryn Mawr

Step into history with a special visit to Bryn Mawr College, where Karen Parshall will give a talk about groundbreaking mathematician, Emmy Noether and how she spent the final chapter of her remarkable life.

In 1933, the German algebraist Emmy Noether (1882-1935) joined the Department of Mathematics at Bryn Mawr College. Renowned as one of the guiding lights behind what became known as modern algebra, Noether had overcome many obstacles. As a woman, she was able to earn a doctoral degree in Germany only after a law was passed 1908.Then, as a woman, she was denied the right to apply for the credential that would have allowed her to teach in 1915.Only thanks to the intervention of two heavyhitters--- Felix Klein and David Hilbert-did she finally succeed in getting a paid teaching job in 1923. Ten years later, however, the Nazis revoked the right to teach for all Jews. Friends in the United States secured her the position at Bryn Mawr that she held for less than two years, owing to her untimely death.

Learn more click here. 

7:15 PM – 8:15 PM Terrace Ballroom Special Plenary Lecture

The Shape of Math to Come

We present an overview of how certain computational tools currently interact with mathematical practice, and reflect on the implications for research mathematics in the short to medium term, as the field navigates the emerging age of AI and formal verification systems.

Tuesday, July 28, 2026

9:00 AM – 6:00 PM Hall E - Expo Expo and Collaborations

Exhibition & Collaboration

9:00 AM – 10:00 AM Terrace Ballroom Plenary Lecture

Uniformization Theorems and Related Results in Higher-Dimensional Complex Geometry

We give an overview of uniformization theorems and related results in higher-dimensional complex geometry in which one recovers the complex structure of model complex manifolds such as Hermitian (locally) symmetric manifolds of the semisimple type and rational homogeneous manifolds, together with results characterizing distinguished subvarieties on such complex manifolds by imposing topological, geometric (notably curvature) or analytic conditions, or a combination of such conditions. We emphasize the roles of several complex variables, complex differential geometry, CR geometry, Lie theory, algebraic geometry, partial differential equations, harmonic analysis and ergodic theory and their interplay in various results of the author's in part with collaborators in which also techniques developed for the study of the case of model manifolds of positive curvature find their applications to the solution of problems for the case of negative curvature through the geometric theory of uniruled projective manifolds and their uniruled projective subvarieties.
10:15 AM – 11:15 AM Terrace Ballroom Plenary Lecture

Hardy Spaces of Holomorphic Functions and Explicit Formulae for A Class of Integrable Partial Differential Equations

We obtain explicit formulae for a class of integrable partial differential equations involving nonlocal terms, using Lax pairs of operators acting on Hardy spaces of holomorphic functions. Applications include an approach of the soliton resolution conjecture and a description of the small dispersion limit for the Benjamin-Ono equation, as well as the construction of the flow map on the energy space of the half-wave maps system. Dedicated to the memory of Peter David Lax (1926--2025)
10:30 AM – 10:50 AM 116-A Short Communications

Determinants of Mahler Measures and Special Values of L-Functions

In this talk, we will present some recent results about Mahler measures of two families of bivariate polynomials, namely $P_t=x+x^{-1}+y+y^{-1}+\sqrt{t}$ and $Q_t=x^3+y^3+1-\sqrt[3]{t}xy$. In the cases when the zero loci of these polynomials define CM elliptic curves over number fields, we derive general formulas for their Mahler measures in terms of $L$-values of cusp forms. For each family, we also classify all possible values of $t$ in number fields of degree not exceeding $4$ for which the corresponding elliptic curves have complex multiplication. Finally, for all such values of $t$ in totally real number fields of degree $n=2$ and $n=4$, corresponding to elliptic curves $\mathcal{F}_t$ (resp. $\mathcal{C}_t$), we prove that determinants of $n\times n$ matrices whose entries are Mahler measures corresponding to their Galois conjugates are non-zero rational multiples of $L^{(n)}(\mathcal{F}_t,0)$ (resp. $L^{(n)}(\mathcal{C}_t,0)$).
10:30 AM – 10:50 AM 119-AB Short Communications

Eigenvalue Lower Bounds for Laplacians

In this talk, we present new results concerning lower bounds on the first eigenvalue for the Laplace operators, especially under variable-component Robin boundary conditions. We not only derive novel results for the Robin Laplacian but also significantly improve existing bounds over those for the Dirichlet Laplacian. The methodology adopted in our study is further extended to establish new lower bounds on the first eigenvalue of the polyharmonic Dirichlet operator. This talk is based on our joint work with Rupert L. Frank (Caltech and LMU Munchen) and Ari Laptev (Imperial College London).
10:30 AM – 10:50 AM 115-C Short Communications

Emerging Works on Hahn Difference Equations and Oscillation

Oscillation theory for difference equations involving the full Hahn operator remains largely unaddressed in the literature, despite extensive work on the qualitative analysis of solutions. While significant progress has been made in spectral and asymptotic properties, dedicated oscillation criteria are notably absent. Historical research has focused on transform methods and solution techniques, such as the Fourier–Hahn transform for quantum models, rather than oscillatory behavior. Even recent advances—including the adaptation of the Asymptotic Iteration Method and applications of Nevanlinna theory—provide powerful tools yet do not directly confront oscillation phenomena. In this talk, we initiate the systematic study of oscillation for such equations by establishing foundational, classical oscillation theorems for the second-order case.
10:30 AM – 10:50 AM 118-AB Short Communications

Fixed Superalgebras, Supertraces, and Structural Properties via Graded Embeddings

\begin{document}\titulo{Fixed Superalgebras, Supertraces, and Structural Properties via Graded Embeddings}\autores{Claudemir Fideles Bezerra Jr. \\ UNICAMP (Brazil)}\maketitle\thispagestyle{empty}{\selectlanguage{english}\begin{abstract}Let $K$ be a field of characteristic zero, and let $E$ denote the infinite-dimensional Grassmann algebra over $K$. In this talk, we present recent results on algebras that can be embedded into the tensor product of a graded-central-simple algebra $A$ with a supercommutative superring. Under suitable hypotheses, if a supertrace algebra $B$ belongs to the same PI-variety as $A \otimes E$, then $B$ admits an embedding into $A \otimes \Xi$, where $\Xi$ is the so-called $A$-universal supermap of $B$—a supercommutative algebra compatible the supertrace structure of $B$. This embedding holds whenever $B$ satisfies all supertrace identities of $A \otimes E$.As a consequence, we show that if $B$ is finitely generated as an algebra, then its Baer and Jacobson radicals coincide, and its Gelfand–Kirillov dimension is always an integer.These structural findings also contribute to the understanding of the interplay between geometry and the theory of polynomial identities. In particular, we draw inspiration from classical results of Susan Montgomery, who demonstrated that under certain conditions, a ring can inherit polynomial identities from its fixed subrings under group actions—especially when the subring is a centralizer.This presentation is based on joint work with Charles Almeida and Lucio Centrone, supported by FAPESP grant No. 2023/04011-9. These results are new, and are currently submitted.\end{abstract}\begin{thebibliography}{99}\bibitem{ACF2024} C. Almeida, L. Centrone, C. Fideles, {\it Embedding theorems as a bridge between supertraces and supergeometry}, Submitted.\bibitem{ACF2025} C. Almeida, L. Centrone, C. Fideles, {\it Superring extensions and fixed subalgebra structures}, Submitted.\bibitem{mont2} S. Montgomery, Fixed rings of finite automorphism groups of associative rings, Lecture Notes in Mathematics, vol. 818, Springer, Berlin, 1980.\end{thebibliography}}\end{document}
10:30 AM – 10:50 AM 118-C Short Communications

Hausdorff Dimension in Fractal Analysis

We reveal a surprising independence between arithmetic and fractal properties of real numbers by studying the interplay between irrationality exponents and fractal dimensions. For any prescribed parameters, we explicitly construct Cantor-like sets in which almost every point attains a given irrationality exponent, while the set itself has a specified Hausdorff dimension. We further extend this framework to the effective Hausdorff dimension of individual real numbers. These constructions employ a carefully designed tree method, allowing simultaneous control over Diophantine approximation and fractal complexity.Our results bridge classical Diophantine approximation with fractal geometry and algorithmic information theory, showing that rational approximation rates and fractal structure can be independently tuned. By extending the metric results of Jarník and Besicovitch, we uncover deep connections between arithmetic properties and geometric or computational complexity. This approach not only clarifies the relation between irrationality and fractal dimensions but also introduces versatile techniques for studying randomness, computability in number theory, and the fine structure of exceptional sets.
10:30 AM – 10:50 AM 115-B Short Communications

Smoothness of Local Conjugation of Normal Forms on Non-Smooth Spaces

Local conjugation of normal forms is a frequently used technique in the qualitative analysis of dynamical systems. The question of smoothness of the conjugation arises in many applications. We discuss the preservation of smoothness in neighborhoods of a fixed point or an invariant manifold, with respect to variables and parameters. We also discuss the relation of smoothness to the spectral gap and non-resonance condition. Our development of the blid map localization method allows us to discuss the smoothness of the conjugation on some non-smooth (Banach) spaces. The blid map method can also possibly be applied to the question of partition of unity on non-smooth spaces, which we include in the list of open problems in the conclusion of this talk.
10:30 AM – 10:50 AM 120-AB Short Communications

Strong Convergence of New Iterative Methods for Quasi-Monotone Variational Inequalities

We consider variational inequalities with quasi-monotone and Lipschitz continuous operators in a Hilbert space. We introduce two new algorithms and show the strong convergence of the generated sequence to a solution of the variational inequality problem, both with the knowledge, as well as without any knowledge of the Lipschitz constant of the operator. We give also some examples of applications and numerical experiments of our main results and compare the speed of convergence of the two methods.
10:30 AM – 10:50 AM 115-A Short Communications

Strongly Adapted Contact Geometry of Anosov 3-flows

We will discuss some recent developments in the contact geometric theory of Anosov 3-flows, whose roots go back to the works of Mitsumatsu and Eliashberg-Thurston in the mid 1990s. In particular, we provide a contact geometric characterization of Anosov 3-flows based on interactions with Reeb dynamics, as well as investigate some properties of the resulting geometries. We will briefly highlight how these results allow one to re-approach some classical open questions in Anosov dynamics.
10:50 AM – 11:10 AM 120-AB Short Communications

A Novel Approximation Method for Solving Split Variational Inequality Problem Beyond Monotonicity

In this talk, we present a novel iterative method for solving Split Variational Inequality Problem (SVIP) in real Hilbert spaces. Our proposed method is without any product space formulation and with monotonicity assumption on the SVIP associated operators dispensed. The convergence analysis of these methods and some numerical examples to illustrate this method are discussed.This is joint work with Grace N. Ogwo and Chinedu Izuchukwu (My Ex- PhD students and Postdoc).
10:50 AM – 11:10 AM 118-C Short Communications

Boundedness of Composition Operators on Higher-Order Besov Spaces

We study the boundedness of composition operators on inhomogeneous Besov spaces of higher-order smoothness.Composition operators arise naturally in the context of changes of variables and are also referred to as Koopman operators or pull-back.Their boundedness plays an important role in the analysis of dynamical systems, the theory of function spaces on domains, and partial differential equations.In this work, we provide a characterization of boundedness for composition operators on Besov spaces $B^s_{p,q}$ with $s > 1 + 1/p$ on the one-dimensional Euclidean space.In contrast to the lower-order case $0 < s < 1$, for which the theory is well developed,there have been few results addressing the boundedness of composition operators in the higher-order regime $s > 1$.Our approach reveals a fundamental connection between composition operators and pointwise multipliers of Besov spaces.We show that, in the higher-order setting, the boundedness of composition operators is intrinsically governedby multiplier properties, and we effectively exploit existing characterizations of pointwise multipliers.As a result, we obtain necessary and sufficient conditions for the boundedness of composition operators on Besov spaces with $s > 1 + 1/p$.We also establish a similar characterization for the boundedness of composition operators on Sobolev spaces.
10:50 AM – 11:10 AM 115-A Short Communications

Finitistic Dimension and Singularity Categories

Let A be a Noetherian ring (not necessarily commutative). When is there a uniform upper bound on the projective dimensions of all (left) A-modules of finite projective dimension? When A is commutative, it follows from the works of Bass and Raynaud-Gruson, that this is the case if and only if A has finite Krull dimension. The question of whether such a uniform upper bound exists for Artin algebras, even when restricted to finitely generated modules only, was first publicized by Bass in the 1960s. This question, since known as the finitistic dimension conjecture, remains open even after half a century. In this talk, based on ongoing joint work with Jan Stovicek, we will present some criteria for the existence of such uniform upper bounds in terms of certain form of generation in module category and singularity category. One ingredient of our approach is based on certain generalizations of the ”delooping level” of Gelinas.
10:50 AM – 11:10 AM 119-AB Short Communications

Solving Riemann Problems Using Topological Tools

We present a detailed construction and application of a topological framework to solve Riemann problems for systems of conservation laws. Central to this approach is the concept of the wave manifold, a differentiable three-dimensional manifold whose points represent shock and rarefaction waves. Unlike classical methods, where wave curves in state space may overlap or intersect, the wave manifold disentangles these curves and provides a geometric setting in which admissibility conditions and wave interactions can be systematically analyzed.We focus on a specific two-component system with quadratic flux function. The wave manifold is constructed explicitly using adapted coordinates and a blow-up transformation that resolves the singularity at coinciding left and right states. The resulting manifold allows us to define and visualize key structures, such as Hugoniot curves, rarefaction foliations, sonic and characteristic surfaces, and regions of shock admissibility. These are explored analytically and graphically to understand their role in constructing Riemann solutions.A major contribution of this study is the use of topological tools to classify and analyze admissible waves. The wave manifold is subdivided into distinct regions by the characteristic and sonic surfaces, and the boundary of shock admissibility is precisely determined. Composite wave structures, involving both shock and rarefaction elements, are identified and traced through foliations within these regions. The intersection of wave surfaces in the manifold determines the structure of Riemann solutions, which are obtained by combining slow and fast wave families through a geometrically constructed intermediate surface.We apply this method to solve Riemann problems, highlighting how the topology of the wave manifold encodes admissibility and resolves ambiguities that arise in state space. The visualizations of the wave curves and surfaces offer new insights into the behavior of nonlinear wave patterns, particularly in systems where strict hyperbolicity is lost in regions of the state space.This work builds upon and extends earlier developments in the topological treatment of conservation laws, offering a complete and computable structure for understanding and solving Riemann problems in quadratic systems. The approach has implications for the study of degenerate systems, composite wave interactions, and the design of numerical methods for complex PDE models.
10:50 AM – 11:10 AM 118-AB Short Communications

Study on Chain Conditions in Modules and Rings

In this talk we would like to explore the study of ascending/ descending chain condition of variants of module and ring structures. Here we will try to explore several properties of Artinian/ Noetherian modules and rings and their generalizations in the various context of chain condition, also trying to establish the relationship of these modules with injective/ projective modules. Further, we will focus on well-known Hopkins-Levitzki theorem and Hilbert’s Basis theorem.We investigate whether Hopkins-Levitzki Theorem extend to semi-projective/ semi-injective modules. Unfortunately the answer we have is negative; counter examples are provided. However it is shown that, the answer is positive for certain large classes of semi-projective/ semi-injective modules.
10:50 AM – 11:10 AM 115-C Short Communications

The Structure of $(R,S)$-Semimodules Over Hemirings

In ring theory, the bimodule structure has been extended to a $(K,L)$-module, where every $(K,L)$-bimodule is a $(K,L)$-module, but the converse holds only when the rings $K$ and $L$ possess central idempotents. The generalization of this concept to a hemiring $R$, a hemiring $S$, and a commutative additive monoid $(M,+)$ yields an $(R,S)$-bisemimodule. However, the structure of an $(R,S)$-semimodule, as a natural generalization of a bisemimodule, has not been extensively explored, even though it is essential for the development of radical theory and the study of non-unital structures in algebra. This study constructs an $(R,S)$-semimodule over a hemiring as a generalization of an $(R,S)$-bisemimodule. The choice of hemirings ensures that the resulting $(R,S)$-semimodule does not trivially reduce to a bisemimodule (as may occur in the case of semirings). Furthermore, the constructions of $(R,S)$-subsemimodules, cyclic $(R,S)$-semimodules, factor $(R,S)$-semimodules, and multiplication $(R,S)$-semimodules are presented, along with their main properties. These results enrich module theory over hemirings and open further research opportunities on primeness and its generalizations, prime radicals, and the duality of primeness within the structure of $(R,S)$-semimodules.
10:50 AM – 11:10 AM 115-B Short Communications

Where Dynamics Meet Order: Recurrence in Riesz Spaces

Ergodic theory is a rich and fascinating area of mathematics, traditionally developed in a measure-theoretic framework. In this presentation, we move beyond the classical setting and explore a measure-free approach based on Riesz spaces. Building on the formulations of Poincaré, Kac, and Kakutani–Rokhlin theorems, we extend fundamental results on recurrence and ergodicity, highlighting their broader significance. This perspective not only unifies classical ideas but also leads to new results in probabilistic contexts that go beyond the traditional framework. The talk is designed to provide both an accessible introduction to the subject and an overview of recent advances, inviting the audience to discover how ergodic theory continues to evolve and expand across mathematical disciplines.This talk is based on joint works with Y. Azouzi, M. A. Ben Amor, J. Homann and B. A. Watson.
10:50 AM – 11:10 AM 116-A Short Communications

Zariski Density of Grand Orbit Transversals in Arithmetic Dynamics

Let $f:X\to{X}$ be an endomorphism of a smooth projective variety $X$ defined over a number field $K$, and assume that $X(K)$ is Zariski dense in $X$. Each point $P\in{X(K)}$ determines a grand orbit\[\mathcal{O}_f^{\textup{grand}}(P) := \bigl\{ Q\in X(K) : f^n(Q)=f^m(P)~\text{for some $m,n\ge0$} \bigr\}.\]Distinct grand orbits are disjoint, so they define a dynamical orbital partition of $X(K)$. An $\textit{$f$-transversal of $X(K)$}$ is a subset $T\subseteq{X(K)}$ that contains exactly one point from each grand orbit. We ask to what extent $f$-transversals are large. More precisely, we say that a triple $(X,K,f)$ is $\textit{weakly transversal}$ (respectively $\textit{strongly transversal})$ if, after replacing $K$ with a finite extension, there exists at least one Zariski dense $f$-transversal (respectively, if every $f$-transversal is Zariski dense). Weak and strong transversality quantify the idea that the collection of orbits should be widely spaced, and thus the two transversality properties are in some sense orthogonal to the more widely studied problem of density of individual orbits. We will describe recent work proving weak transversality for $\mathbb{P}^n$ and for K3 surfaces and strong transversality for linear maps of $\mathbb{P}^n$ and for abelian varieties, highlighting the variety of methods employed in the proofs. As time permits, we will discuss stronger properties that use only transversals formed by taking one point from each Zariski dense grand orbit. [Joint work with Hector Pasten]
11:10 AM – 11:30 AM 115-B Short Communications

Analytical Model for Impact Pressure Coefficient and Object Mobilization Length in Landslides

Motion of a movable obstacle is initiated when the impact pressure exerted by alandslide exceeds the basal frictional resistance of the obstacle and persists as long as the force applied remains dominant. Using a force-energy framework, we deriveclosed-form expressions for the impact pressure coefficient $C_p^0$ and themobilization length $L$ characterizing the flow-obstacle interaction.A dimensionless number called the obstacle mobilization number is introduced as the ratioof the obstacle shear resistance to the flow kinetic energy andis shown to be related to the obstacle Froude number $Fr_0$. As the obstacletranslates a distance $L$, its kinetic energy is dissipated by basalfriction until the obstacle comes to rest. Equating the initial kinetic energy with the frictionalwork yields an explicit expression for $L$. Conversely, prescribing $L$ allowsthe estimation of the impact velocity $u_p$, providing a practical method forvelocity estimate in landslides.The model predicts that $C_p^0$ decreases strongly to weakly nonlinearly with increasing impact velocity, particle-obstacle density ratio,and grain-covered area, while increasing linearly with basal friction.$C_p^0$ is highly sensitive to obstacle geometry (shape). The mobilizationlength scales as $L \propto u_p^2$, decreases with increasing basal frictionand the gravitational acceleration component normal to the flow depth.Laboratory chute experiments using Nepalese fruit seeds and food grains confirmsound agreement with our analytical model predictions. Applications include hazardmitigation, protective structure design, and granular transport in process engineering.
11:10 AM – 11:30 AM 115-C Short Communications

Cleanness of Modules from Grothendieck Category Point of View

Clean module is defined as a generalization of clean ring. Since a module does not necessary have a multiplication, the definition of clean module is obtained from its homomorphisms ring. It has already well known the necessary and sufficient condition of clean module, which was introduced by some previous authors, for example in Lemma 2.1 and Proposition 2.2 of Camillo et al. [2]. The theorem is very useful for guiding observation of cleanness in other structures, for example for clean comodules or clean coalgebras. However, we propose a different approach, namely using some properties in Grothendieck category, such that we obtain a more general proof of the necessary and sufficient condition of clean module. Moreover, we can extend our observation in any Grothendieck category to get a categorical “clean” element.
11:10 AM – 11:30 AM 120-AB Short Communications

Conformal Welding: Old and New

Conformal welding homeomorphisms are circle homeomorphisms that arise naturally in Teichmuller theory, Mathematical physics and dynamics. It is well known that not every circle homeomorphism is a conformal welding. However, in this talk we will see that every orientation-preserving circle homeomorphisms is the composition of two conformal weldings, which implies that conformal weldings are not closed under composition. Our approach uses the log-singular maps introduced by Bishop, which are conformal weldings. We will also see that for such conformal weldings, the so-called welding correspondence is highly non-injective, which associated Jordan curves of Hausdorff dimensions ranging from 1 to 2.
11:10 AM – 11:30 AM 118-AB Short Communications

Explicit Images for the Shimura Correspondence

For $(r, 6) = 1$ with $1 \leq r \leq 23$, and a non-negative integer $s$, we define\[\mathcal{A}_{r,s, N, \chi} = \{ \eta(z)^{r} f(z) : f(z) \in M_{s}(N, \chi)\}.\]In 2014, Yang showed that for $F \in \mathcal{A}_{r, s, 1, 1_N}$, the $r$-th Shimura image associated to the theta-multiplier $\textup{Sh}_{r}(F \mid V_{24}) = G \otimes \chi_{12}$ where $G\in S^{new}_{r+2s - 1}\left(6, - \left( \frac{8}{r} \right), - \left( \frac{12}{r} \right)\right)$. He proved a similar result for $(r,6) = 3$.\:His proofs rely on trace computations in integral and half-integral weights. In this talk, we provide a constructive proof of Yang's result. We obtain explicit formulas for $\mathcal{S}_{r}(F)$, the $r$-th Shimura lift associated to the eta-multiplier defined by Ahlgren, Andersen, and Dicks, when $1\leq r\leq 23$ is odd and $N = 1$. We also obtain formulas for lifts of Hecke eigenforms multiplied by theta-function eta-quotients and lifts of Rankin-Cohen brackets of Hecke eigenforms with theta-function eta-quotients.
11:10 AM – 11:30 AM 119-AB Short Communications

Navier–Stokes Equation in a Cone with Cross-Sections in the Form of 3D Spheres, Depending on Time, and the Corresponding Basis

The report establishes the unique solvability of a boundary value problem for a 3D linearizedsystem of Navier–Stokes equations in a degenerate domain represented by a cone. The domaindegenerates at the vertex of the cone at the initial moment of time, and, as a consequence of this fact,there are no initial conditions in the problem under consideration. First, the unique solvability of theinitial-boundary value problem for the 3D linearized Navier–Stokes equations system in a truncatedcone is established. Then, the original problem for the cone is approximated by a countable family ofinitial-boundary value problems in domains represented by truncated cones, which are constructedin a specially chosen manner. In the limit, the truncated cones will tend toward the original cone. TheFaedo–Galerkin method is used to prove the unique solvability of initial-boundary value problemsin each of the truncated cones. By carrying out the passage to the limit, we obtain the main resultregarding the solvability of the boundary value problem in a cone.
11:10 AM – 11:30 AM 118-C Short Communications

Pseudo Almost Periodic Solution for Some Differential Equations with Piecewise Constant Argument and Applications

In this talk, I will prove several key results regarding the existence and uniqueness of doubly measure pseudo-almost periodic solutions for differential equations with piecewise constant arguments. To achieve this, we will utilize the properties of almost periodic functions with measure and apply the Banach fixed point theorem. Furthermore, we will illustrate these findings with various examples.
11:10 AM – 11:30 AM 115-A Short Communications

Some Problems in Algebra, Number Theory and Combinatorics

\documentclass[12pt,a4paper]{article}\usepackage{amsmath, amssymb}\usepackage{graphicx}\usepackage{hyperref}\usepackage{booktabs}\usepackage{siunitx}\usepackage{caption}\newcommand{\R}{\mathbb{R}}%\newcommand{\Q}{\mathbb{Q}}%\newcommand{\N}{\mathbb{N}}%\title{Some problems in algebra, number theory and combinatorics}\author{Tserendorj Dashdorj\\National University of Mongolia, Mongolia\\[2ex] {\it dashdorjtserendorj814@gmail.com}}\date{}\begin{document}\maketitle\begin{itemize} \item[] \textbf{Problem 1.} Prove the theorem from references \cite{Dashdorzh1988} and \cite{Dashdorzh1994} without the restriction $\frac12\in \Phi.$ \item[] \textbf{Problem 2.} Find all forms of algebraic numbers that cannot be expressed using finite radicals \cite{Enkhbold1982}. \item[] \textbf{Problem 3.} Let $R=q\sqrt{D},$ where $0
11:10 AM – 11:30 AM 116-A Short Communications

The Lean Landscape of AI-Assisted Asymptotic Analysis

  • Omar Shehab (In transition)
Recent advances in AI-assisted theorem proving have shown that modern proof assistants, when coupled with large language models, can support professional-level reasoning in mathematics. Yet asymptotic analysis—the language of limits, scaling, and regimes underlying algorithms, numerical methods, and computational complexity—remains largely informal and outside the reach of current systems. This gap is striking, given that asymptotic reasoning governs scalability, convergence, and hardness in both theory and applications. We argue that the Lean ecosystem has reached a level of maturity where AI-assisted, formally verified asymptotic analysis is now feasible, while also highlighting the epistemic risks that arise when formalization itself becomes automated and distributed. State-of-the-art AI theorem provers excel at bounded arguments but lack the conceptual machinery required for dominance reasoning, limit processes, recurrence relations, probabilistic asymptotics, and average-case ensembles. At the same time, emerging AI systems can already propose correct domain decompositions and asymptotic inequalities when guided appropriately. What remains missing is a principled framework that turns such proposals into certified, reusable proof objects.Lean provides a natural verification backbone: its mature real analysis, limit theory, and expanding automation allow sophisticated asymptotic arguments to be expressed and checked. However, formal verification should not be conflated with conceptual correctness. Formal code can trivialize results through misspecified definitions or succeed for unintended reasons. As AI systems generate increasing volumes of formal proofs, these epistemic failure modes become more salient, not less. Looking ahead, AI-assisted asymptotic analysis will develop in a fundamentally distributed manner. Multiple groups may formalize conceptually equivalent results using incompatible abstractions, creating redundancy and semantic fragmentation despite local correctness. Addressing this requires advances in formal epistemology: methods for detecting conceptual equivalence, tracking provenance, and ensuring interoperability across formal developments.The convergence of a mature Lean ecosystem and AI systems capable of long-horizon reasoning makes asymptotic analysis a natural next frontier. Success will depend not only on automation, but on preserving meaning and interoperability as mathematics becomes increasingly machine-mediated.
11:30 AM – 11:50 AM 118-AB Short Communications

A Quantitative Solution to Hilbert’s Tenth Problem: Universal Pairs and Formal Verification

  • Marco David (University of California, Berkeley)
This talk explores two themes: bounding the complexity of Diophantine equations over the integers, which provides a quantitative negative solution to Hilbert’s Tenth Problem, and developing mathematical proofs with the assistance of interactive theorem provers. Hilbert's Tenth Problem asks about the decidability of Diophantine equations and has been answered negatively by Davis, Putnam, Robinson and Matiyasevich. It is natural to ask for which subclasses of Diophantine equations Hilbert's Tenth Problem remains undecidable. Such subclasses can be defined in terms of universal pairs: simultaneous bounds on the number of variables $\nu$ and degree $\delta$ such that all Diophantine equations can be rewritten in at most this complexity. Our work develops explicit universal pairs $(\nu, \delta)$ for integer unknowns, achieving new bounds that cannot be obtained by naive translations from known results over the natural numbers.In parallel, we have conducted a formal verification of our results using the proof assistant Isabelle. While formal proof verification has traditionally been applied a posteriori to known results, this project integrates formalization into the discovery and development process. We also describe key insights gained from this unusual approach and its implications for mathematical practice. Our work contributes both to the study of Diophantine equations and to the broader question of how mathematics is conducted in the 21st century.
11:30 AM – 11:50 AM 116-A Short Communications

Adaptive Coarse Spaces for High-Contrast and Multiscale Coefficients for Problems in H(grad)

  • Juan Gabriel Calvo Alpizar (Universidad de Costa Rica)
We present a domain decomposition preconditioner for second-order elliptic partial differential equations that handles coefficients with high-contrast and multiscale properties, and is suitable for irregular subdomains. We will present partition of unity functions and appropriate eigenvalue problems that enrich usual coarse spaces. We demonstrate that the condition number of the preconditioned systems is bounded with a bound that is independent of the contrast, and include selected numerical experiments that confirm the robustness of our preconditioner.
11:30 AM – 11:50 AM 118-C Short Communications

Existence and Multiplicity Results for Concave-Convex Type Problems Involving the One-Dimensional $\phi$-Laplacian

  • Uriel Kaufmann (FaMAF, UNC)
Let $\Omega=(a,b)\subset\mathbb{R}$, $0\leq m,n\in L^{1}(\Omega)$,$\lambda,\mu>0$ be real parameters, and $\phi:\mathbb{R}\rightarrow\mathbb{R}$be an odd increasing homeomorphism. In this talk we consider the existence ofpositive solutions for problems of the form\[%\begin{cases}-\phi\left( u^{\prime}\right) ^{\prime}=\lambda m(x)f(u)+\mu n(x)g(u) &\text{ in }\Omega,\\u=0 & \text{ on }\partial\Omega,\end{cases}\]where $f,g:[0,\infty)\rightarrow\lbrack0,\infty)$ are continuous functionswhich are, roughly speaking, sublinear and superlinear with respect to $\phi$,respectively. The assumptions on $\phi$, $m$ and $n$ are substantially weakerthan the ones imposed in previous works. The approach used here combines theGuo-Krasnoselskii fixed-point theorem, the sub-supersolutions method, andsome estimates on related nonlinear problems.
11:30 AM – 11:50 AM 115-B Short Communications

Generalized Stuart-Landau Oscillator in Any Dimension

  • Debashis Ghoshal (Jawaharlal Nehru University)
The two-dimensional Stuart-Landau equation provides a paradigmatic model of nonlinear oscillation that exhibits Hopf bifurcation. Using Clifford algebra, we propose a generalization to arbitrary dimensions that retains its essential features, namely, its exact solvability and symmetries. The asymptotic behaviour of possible trajectories, limit cycles and basins of attraction will be discussed. We shall briefly comment on related problems, including coupled oscillators, parametric modulation, reduction of symmetries, etc. This talk is based on joint work with P. Bhuyan Gogoi, R. Ghosh, A. Patel, A. Prasad and R. Ramaswamy (Phys. Rev. E110 (2024) L032202 and Phys. Rev. E112 (2025) 054221).
11:30 AM – 11:50 AM 119-AB Short Communications

Hopf Conjecture for Gaussian Curvature of Minimal Graphs

  • David Kalaj (University of Montenegro)
In this paper, we solve the longstanding Gaussian curvature conjecture of a minimal graph $S$ over the unit disk. The conjecture asserts that for any minimal graph above the unit disk, the Gaussian curvature at the point directly above the origin satisfies the sharp inequality \( |\mathcal{K}| < \frac{\pi^2}{2} \). We first reduce the conjecture to the problem of estimating the Gaussian curvature of certain Scherk-type minimal surfaces defined over bicentric quadrilaterals inscribed in the unit disk, containing the origin. We then provide a sharp estimate for the Gaussian curvature of these minimal surfaces at the point above the origin. Our proof employs complex-analytic methods, as the minimal surfaces in question allow a conformal harmonic parameterization.
11:30 AM – 12:30 PM Terrace Ballroom Plenary Lecture

Modern Machine Learning Methods: Large Step-Size Optimization, Implicit Bias, and Benign Overfitting

  • Peter Bartlett (University of California, Berkeley and Google DeepMind)
The impressive performance of modern machine learning methods seems to arise through different mechanisms from those of classical statistical learning theory, mathematical statistics, and optimization theory. Simple gradient methods find excellent solutions to non-convex optimization problems, and without any explicit effort to control model complexity they exhibit excellent prediction performance in practice. This talk will describe recent progress in statistical learning theory and optimization theory that demonstrates the optimization benefits of step-sizes that are too large to allow gradient methods to be viewed as an accurate time discretization of a gradient flow differential equation, that characterizes the solutions that are favored by gradient optimization methods, and that illustrates when those solutions can overfit training data but still provide good predictive accuracy.
11:30 AM – 11:50 AM 115-C Short Communications

On the Odd Unitary Analogue of Gram-Schmidt Process

  • Aparna Pradeep Vadakke Kovilakam (Indian Institute of Technology Madras, India)
The Gram-Schmidt process introduced by J.P. Gram and E. Schmidt enables one to orthonormalize a set of vectors in an inner product space. Using this, one can transform a square matrix to an orthogonal matrix by an upper triangular matrix. This motivated L.N. Vaserstein to introduce a similar method for symplectic matrices in 1976. For a given alternating matrix ϕ of size 2n, Vaserstein proved the existence of two elementary matrices of size 2n−1, which can be modified to get symplectic matrices with respect to ϕ. In our recent paper, we defined a set of matrices analogous to Vaserstein-type matrices, for Petrov’s odd unitary group, which is a generalization of all classical groups. We proved that these are elementary linear matrices, and these matrices belong to Petrov’s odd unitary group under some conditions. We also proved that these matrices generate Petrov’s odd elementary hyperbolic unitary group when the ring is commutative. Thus our construction gives a new set of generators for the odd elementary hyperbolic unitary group and thereby visualizing this group in a simpler form. We have also proved that the elementary matrices in the odd unitary analogue of the Vaserstein’s construction form a set of generators for the elementary linear group. I would like to discuss this result in detail.
11:30 AM – 11:50 AM 120-AB Short Communications

Pfaffian Equations: A Variational Perspective

  • Pablo Pedregal (Universidad de Castilla-La Mancha)
Pfaffian equations are part of a classic area well-established in Differential Geometry. From a more analytical viewpoint, it has been traditionally treated in textbooks dealing with Differential Equations focusing on analytical techniques to understand and, eventually, find solutions. As usual, the success of those methods are however limited to explicit situations where computations can be carried out to the end. There are some general existence and uniqueness results as well. Yet the numerical approximation of such solutions has not been, to the best of our knowledge, treated. By means of a variational approach based on a true vector variational problem, we propose a mechanism to examine and numerically approximate such solutions, explore its remarkable properties, and test its practical performance in a number of explicit examples. The method can be implemented in situations where the underlying field defining the Pfaffian equation is not known exactly, but may be part of a broader approximation scheme.
11:30 AM – 11:50 AM 115-A Short Communications

Pro-Representability of Chow Groups and Hodge Numbers

  • Sen Yang (Chuzhou University)
In this talk, I will discuss the pro-representability of the Chow group $CH^{p}(X)$, where $X$ is a smooth projective variety over a number field $k$. When certain Hodge numbers of $X$ vanish, namely, $H^{p}(X,\Omega^{i}_{X/k})=H^{p+1}(X,\Omega^{i}_{X/k})= \cdots =H^{2p-1-i}(X,\Omega^{i}_{X/k})=0$ for $i$ such that $0 \leq i \leq p-2$, we prove that the formal completion $\widehat{CH}^{p}(A)$ of $CH^{p}(X)$ at a local augmented Artinian $k$-algebra $A$ with the maximal ideal $m_{A}$ satisfies\[\widehat{CH}^{p}(A) \cong H^{p}(X, \Omega^{p-1}_{X/ k})\otimes_{k}m_{A}.\]This provides a unified cohomological criterion for the pro-representability of the functor $\widehat{CH}^{p}$, generalizing earlier work by Bloch, Stienstra, and Mackall for $p=2$ and $p=3$. Our result reveals an intrinsic connection between the deformation theory of algebraic cycles and the Hodge structure of $X$.
11:50 AM – 12:10 PM 115-C Short Communications

A New Symbolic Algorithm for the Equidimensional Decomposition of Varieties Defined by Sparse Polynomials

  • Gabriela Jeronimo (Universidad de Buenos Aires)
Sparse polynomials (namely, polynomials with nonzero coefficients only at prescribed sets of monomials) have become a central topic in the computer algebra framework over the last decades, due to their ubiquity in applications and the computational challenge of solving general systems of polynomial equations.We will present a new symbolic probabilistic algorithm that, given asystem of sparse polynomials, $f_1,\dots, f_m$ in $\mathbb{Q}[x_1,\dots, x_n]$, characterizes completely all the equidimensional components of its zero set $V = \{x \in \mathbb{C}^n \mid f_1(x) = 0,\dots , f_m(x) = 0\}$. Based on deformation techniques, the algorithm computes a finite set of representative points for each of the equidimensional components of $V$ within a complexity which is polynomial in combinatorial invariants associated to the supports of $f_1,\dots, f_m$.This is joint work with María Isabel Herrero (Universidad Torcuato Di Tella, Argentina) and Juan Sabia (Universidad de Buenos Aires and CONICET, Argentina).
11:50 AM – 12:10 PM 115-A Short Communications

A Phase Space Localization Operator in Negative Binomial States

  • Zouhair MOUAYN (Sultan Moulay Slimane Universitry)
\documentclass[12pt]{article}\usepackage{amsmath, amssymb}\usepackage{mathrsfs}\begin{document}We investigate the spectral properties of the phase space localization operator $P_{R}$, defined by the indicator function of a disk $D_{R}$ of radius $R < 1$. The localization is performed using a family of \emph{negative binomial states} (NBS), labeled by points $z$ in the unit disk $\mathbb{D}$ and parameterized by $\nu > \frac{1}{2}$. These states are intrinsically connected to the 1D pseudo-harmonic oscillator (PHO) through superpositions of its eigenfunctions. The superposition coefficients form an orthonormal basis of a weighted Bergman space $A^{\nu}(\mathbb{D})$, which also emerges as the eigenspace of a 2D Schrödinger operator with a magnetic field (proportional to $\nu$) corresponding to the lowest hyperbolic Landau level.The eigenvalues $\lambda_{j}^{\nu,R}$ of $P_{R}$ were obtained via a discrete spectral resolution within a shared eigenbasis for $P_{R}$ and the PHO. Using these eigenvalues, we derive a closed-form expression for the variance of the particle count in $D_{R}$ under the determinantal point process (DPP) defined by the weighted Bergman kernel.Beyond $D_{R}$, the phase space content of $P_{R}$ was estimated via the NBS photon-counting distribution, revealing a non-zero residual contribution. Using the coherent state transform associated with NBS, we mapped $P_{R}$ to $A^{\nu}(\mathbb{D})$ and derived its explicit integral kernel $K_{\nu,R}(z,w)$, which converges to the Bergman kernel $K_{\nu}(z,w)$ as $R \to 1$.\end{document}
11:50 AM – 12:10 PM 116-A Short Communications

An Improved Finite Difference Scheme for Magnetohydrodynamic Flows

  • Canan Bozkaya (Middle East Technical University)
This work presents the development and analysis of a finite difference scheme for boundary value problems governed by modified Helmholtz-type equations. The formulation is motivated by magnetohydrodynamic duct flow models, in which the coupled governing equations for the velocity and induced magnetic fields are reformulated as decoupled modified Helmholtz equations. The proposed finite difference approach significantly reduces the discretization errors inherent in classical schemes by employing specially constructed difference formulas for first-order derivatives subject to mixed boundary conditions, as well as for second-order derivatives in one- and two-dimensional settings. Accordingly, truncation errors are removed at the level of the finite difference approximations used for the derivative terms. Numerical results demonstrate that the proposed scheme delivers more reliable solutions than the standard finite difference method on relatively coarse meshes, while mesh refinement remains necessary to accurately capture the solution behavior at large values of physical parameters.
11:50 AM – 12:10 PM 120-AB Short Communications

Composition of Activation Functions and the Reduction to Finite Domain

  • GEORGE ANASTASSIOU (UNIVERSITY OF MEMPHIS)
This work takes up the task of the determination of the rate of pointwiseand uniform convergences to the unit operator of the ”normalizedcusp neural network operators”. The cusp is a compact support activationfunction, which is the composition of two general activation functionshaving as domain the whole real line. These convergences are given viathe modulus of continuity of the engaged function or its derivative in theform of Jackson type inequalities.The composition of activation functions aims to more flexible and powerfulneural networks, introducing for the first time the reduction of infinitedomains to the one domain of compact support.
11:50 AM – 12:10 PM 119-AB Short Communications

Coupled Optimal Results in b-Metric Space with Application to Differential Equation

  • Deb Sarkar (Amity University Kolkata)
B-metric space is one of the generalizations of metric space. We introduce the concept of coupling in non-self mapping in this space. Here, we establish some coupled optimal results in b-metric space supported by suitable examples and consequences. Also, an application of non-linear differential equation has been shown.
11:50 AM – 12:10 PM 115-B Short Communications

Localized Modes of Anti-Plane Shear Wave in an Elastic Ultrathin Layer with Spatially Varying Surface Elasticity Effects: Asymptotic WKB-Method

  • Arindam Nath (Harbin Institute of Technology)
The work deals with localized modes of free anti-plane shear vibration in an elastic, isotropic ultrathin layer with a free upper surface exhibiting spatially varying surface elasticity effects. The constitutive boundary conditions account for variable surface shear stresses and surface inertia within the framework of Gurtin–Murdoch surface elasticity theory at the free upper surface. Using the asymptotic WKB method, a solution of the governing wave equation is constructed in the form of a function that decays away from a straight line along which the wave is localized at the surface. From the first two asymptotic approximations, explicit expressions for the natural frequencies and a parameter characterizing the localization rate are derived. By introducing ratios of the surface shear modulus and surface density to their bulk counterparts as functions of the horizontal coordinate—referred to as internal characteristic dimensions of the free surface or coating—it is shown that incorporation of surface shear stresses and surface inertia leads to a decrease in the natural frequencies. The effect of surface inertia is more prominent compared to surface shear stresses on the natural frequencies. It is also observed that the localization of the surface wave takes place at the point where the surface inertia is maximum.
11:50 AM – 12:10 PM 118-C Short Communications

Multiplicity of Positive Solutions for Quasilinear Problems with Mixed Local-Nonlocal Operator and Concave-Critical Nonlinearities

  • Mousomi Bhakta (Indian Institute of Science Education and Research Pune (IISER Pune))
We study the existence and multiplicity of positive solutions for the following concave-critical problem driven by an operator of mixed order obtained by the sum of the classical $p$-Laplacian and of the fractional $p$-Laplacian, \[\begin{equation}\tag{$\PP_{\lambda,\varepsilon}$} -\Delta_p u+\varepsilon(-\Delta_p)^s u=\lambda|u|^{q-2}u+|u|^{p^*-2}u \;\text{ in }\Omega,\quad u=0 \; \text{ in }\mathbb{R}^N \setminus \Omega,\end{equation}\]where $\Omega\subset\mathbb{R}^N$ is a bounded open set, $\varepsilon\in(0,1]$, $00$, we prove Ambrosetti-Brezis-Cerami type results. In particular, we prove the existence of $\Lambda_\varepsilon$ such that (\textcolor{blue}{$\PP_{\lambda,\varepsilon}$}) has a positive minimal solution for $0<\lambda<\Lambda_\varepsilon$, a positive solution for $\lambda=\Lambda_\varepsilon$ and no positive solution for $\lambda>\Lambda_\varepsilon$. We also prove the existence of $0<\lambda^\#\leq\Lambda_\varepsilon$ such that (\textcolor{blue}{$\PP_{\lambda,\varepsilon}$}) has at least two positive solutions for $\lambda\in(0,\lambda^\#)$ provided $\varepsilon$ small enough. This extends the recent result of Biagi and Vecchi (Nonlinear Anal. 256 (2025), 113795), Amundsen, et al. (Commun. Pure Appl. Anal., 22(10):3139–3164, 2023) from $p=2$ to the general $1
11:50 AM – 12:10 PM 118-AB Short Communications

Submanifolds with Boundary and Stokes' Theorem in Heisenberg Groups

  • Marco Di Marco (ETH Zürich)
We introduce the notion of submanifolds with boundary with intrinsic $C^1$ regularity in the setting of sub-Riemannian Heisenberg groups. We present a Stokes’ Theorem for such submanifolds involving the integration of Heisenberg differential forms introduced by Rumin. Talk based on a joint work with A. Julia, S. Nicolussi Golo and D. Vittone.
12:10 PM – 12:30 PM 118-C Short Communications

2D Rotating Bose–Einstein Condensates at the Critical Speed

  • Dinh Thi Nguyen (VNUHCM University of Science)
We study the minimizers of a magnetic two-dimensional nonlinear Schroedinger (Gross–Pitaevskii) energy functional in a quadratic trapping potential, describing a rotating Bose–Einstein condensate. In the first part, we consider the case of a repulsive interaction potential. We derive an effective Thomas–Fermi-like model in the rapidly rotating limit where the centrifugal force compensates the confinement. The available states are restricted to the lowest Landau level. The coupling constant of the Thomas-Fermi functional is to link the emergence of vortex lattices (the Abrikosov problem). In the second part, we consider the case an attractive interaction potential. When the strength of the interaction approaches a critical value, the system collapses to a profile obtained from the (unique) optimizer of a Gagliardo–Nirenberg interpolation inequality. This was established before in the case of fixed rotation frequency. We extend the result to rotation frequencies approaching, or even equal to, the critical frequency at which the centrifugal force compensates the trap. We prove that the blow-up scenario is to leading order unaffected by such a strong deconfinement mechanism. In particular the blow-up profile remains independent of the rotation frequency.
12:10 PM – 12:30 PM 115-A Short Communications

An Algorithmic Approach to the Cauchy Problem for Einstein's Field Equations

  • Arthur Fischer (University of California, Santa Cruz)
Existence and uniqueness theorems for the Einstein field equations are discussed, using results that utilize first order quasilinear symmetric hyperbolic systems, rather than the usual second order strictly hyperbolic systems. These first order hyperbolic methods were developed by the author together with Professor Jerrold Marsden in the early 1970’s and are now widely used in numerical relativity. Using these results, we approach the Cauchy problem for Einstein's field equations in an algorithmic manner. We reduce the problem to two distinct cases. The base case is the harmonic case, or the classical case, in which the Cauchy data satisfies both the constraint equations and a harmonic coordinate condition, which is then resolved by using the harmonic Ricci tensor. This case was done by Professor Yvonne Choquet-Bruhat in the early 1950's using second order hyperbolic methods rather than the first order methods cited above. In our second case, the Cauchy data does not solve any coordinate condition. We reduce this case to the first case by modifying the Cauchy data to satisfy the harmonic coordinate condition, and then find an intermediate harmonic solution. The general non-unique solution to the original problem is then achieved by pulling back this intermediate solution by any diffeomorphism that also pulls back the non-original intermediate harmonic Cauchy data to the original non-harmonic Cauchy data. The fundamental idea behind this approach is that Cauchy data is non-tensorial since Cauchy data involves the time derivative of the metric. Thus isometric spacetimes have non-isometric Cauchy data. Other aspects of the Cauchy problem are very briefly discussed, including the internal structure of the Ricci tensor, how covariance of the scalar curvature gives rise to the constraints on the Cauchy data, the relation of the Cauchy problem to the Hamiltonian formulation of general relativity, and to the problem of isolating and parameterizing the space of true degrees of freedom for the gravitational field. Our algorithmic approach to the Cauchy problem, together with our use of first order hyperbolic methods, although mainly of theoretical interest, also considerably simplifies numerical relativity, a crucial tool in understanding complex astrophysical phenomena such as black hole interactions and gravitational waves.
12:10 PM – 12:30 PM 115-C Short Communications

Classification and Gauss Composition Using Clifford Invariants

  • VENKATA BALAJI THIRUVALLOOR EESANAIPAADI (Indian Institute of Technology Madras)
(Co-Author: Soham Mondal). To a binary quadratic form with values in a line bundle (over an arbitrary base scheme), we may naturally associate the Clifford pair consisting of its generalised even Clifford algebra and its Clifford bimodule, which are respectively the degree zero and degree one graded pieces of its generalised Clifford algebra. A similarity of such binary quadratic forms (with values in isomorphic line bundles) naturally induces an isomorphism of Clifford pairs, which is an isomorphism of the associated quadratic (even Clifford) algebras and a compatible isomorphism of the associated Clifford bimodules. We show that this association induces a natural functorial correspondence between similarity classes of binary quadratic forms and isomorphism classes of Wood pairs consisting of a quadratic algebra and a traceable module over that algebra. This generalises previous work of Martin Kneser in the affine case and reconciles with the work of Melanie Matchett Wood which involved linear binary forms on the dual modules. We apply our result to describe the Picard group of quadratic algebras, generalising earlier work of Martin Kneser and reconciling with recent work of Melanie Matchett Wood and William Dallaporta on Gauss Composition.
12:10 PM – 12:30 PM 115-B Short Communications

Hydrodynamics of Very Large Rectangular Flexible Plate Floating on Shallow Water

  • Santanu Koley (Birla Institute of Technology and Science - Pilani, Hyderabad Campus)
In the present study, the hydrodynamics associated with the water waves interaction with very large rectangular flexible plate floating in shallow water is studied. The incident waves is considered to be oblique in nature. Parabolic approximation technique is used in the solution methodology of the aforementioned boundary value problem. The effect of the compression on the hydroelastic responses of the flexible plate is considered. The main advantage of the present parabolic approximation over the widely used ray theory is that in the ray theory, the amplitude of the waves changes abruptly along the ray which passes through the corners. However, this particular difficulty can be resolved easily through the parabolic approximation approach. The effect of the compressive force and incident wave angle on the plate deflection will be analyzed. The outcome of the present research is helpful to construct various floating marine structures in the nearshore regions.
12:10 PM – 12:30 PM 120-AB Short Communications

Multidimensional Fuzzy-Random Neural Network Operators (NNOs) Based on Trainable-Symmetrical Activation Dynamics

  • Seda Karateke (Istanbul Atlas University)
In this study, we introduce a family of multidimensional neural network operators (NNOs) based on fuzzy-random quasi-interpolation with symmetric and trainable activation dynamics. We calculate the degree of convergence of the multivariate pointwise and uniform convergences obtained using these operators to the fuzzy-random unit operator in $p$-mean sense. In particular, we shall discuss the advantages of the activation mechanism we use here, which is a trainable half-hyperbolic tangent function, over other activation functions in the literature. Moreover, we incorporate multivariate probabilistic-Jackson-type inequalities using the multivariate Fuzzy-random modulus of continuity when calculating convergence rates. The resulting convergence rates and error estimates demonstrate that this operator family is based on a robust theoretical framework. We present a validation of our theoretical findings through numerical examples and error reduction graphs obtained using the Python 3.9 programming language. As a result, we shall blend the theory used here with today's Artificial Intelligence (AI) perspective and give examples of interesting real-life applications.
12:10 PM – 12:30 PM 115-C Short Communications

Opposite Biases Among Primes Associated with Elliptic Curves

  • Sung Min Lee (Wake Forest University)
Let $E/\mathbb{Q}$ be an elliptic curve and $p$ be a prime of good reduction for $E$. Several results have investigated the distribution of primes in arithmetic progressions for which the reduction, $E_p(\mathbb{F}_p)$ is cyclic or has prime order, showing that such biases depend on the arithmetic structure of $E$.In this talk, we take a statistical perspective by considering a family of elliptic curves rather than a single one. We demonstrate that, on average, the primes with these properties tend to cluster in certain residue classes modulo $n$ more than others. Interestingly, although the condition that $E_p(\mathbb{F}_p)$ has prime order implies that it is cyclic, we find that these two sets of primes exhibit opposite congruence class biases across the family.This is joint work with Dr. Jacob Mayle and Dr. Tian Wang.
12:10 PM – 12:30 PM 118-AB Short Communications

Prediction Models for High-Dimensional Problems: Choose the Data That Matters

  • Kateryna Pozharska (Institute of Mathematics of the National Academy of Sciences of Ukraine)
In the talk we will discuss recovery methods for unknown high-dimensional relations from incomplete data. Namely, we consider both linear (such as weightel least squares) and non-linear (rLasso, basis pursuit, orthogonal matching pursuit) algorithms based on a restricted number of training data (function values at some points) and figure out difficulties and advantages of each of them in a number of model settings.
12:10 PM – 12:30 PM 119-AB Short Communications

The Inhomogeneous Cauchy-Riemann Equation with or Without Dini Continuity

  • Adam Coffman (Purdue University Fort Wayne)
Regarding the interior regularity of the inhomogeneous Cauchy-Riemann equation $\partial u/\partial\bar z=f$, it has been known since the work of Chern, and Hartman and Wintner, that the property of Dini continuity of $f$ is sufficient for the continuity of all first derivatives of $u$. We show by example that $f$ can be continuous and very close to Dini continuous, while $u$ is classically differentiable everywhere and vanishing to infinite order at a point, but $\partial u/\partial z$ is discontinuous. The main application is to the regularity of $J$-holomorphic curves for rough almost complex structures $J$. Joint work with Yifei Pan, Purdue University Fort Wayne.
12:10 PM – 12:30 PM 116-A Short Communications

The Method of Probabilistic Solution for 3D Dirichlet Generalized and Classical Harmonic Problems in Some Finite Bodies with Cavities

  • Tinatin Davitashvili (Ivane Javakhishvili Tbilisi State University)
In this paper, we investigate the application of the method of probabilistic solutions (MPS) to numerical solving of Dirichlet generalized and classical harmonic problems in some finite bodies with cavities. The term "generalized" indicates that a boundary function has a finite number of first kind discontinuity curves. The suggested algorithm for numerical solution of boundary problems consists of the following stages: a) application of the MPS, which in its turn is based on a computer modeling of the Wiener process; b) finding the intersection point of the trajectory of the simulated Wiener process and the surface of the problem domain; c) developing a code for numerical implementation and verifying the accuracy of the results; d) finding of the probabilistic solution of generalized problems at any fixed points of the considered domains. The algorithm does not require approximation of a boundary function. To illustrate the effectiveness and simplicity of the proposed method five examples are considered. Numerical results are presented and discussed.
12:30 PM – 1:30 PM Benjamin Franklin Stage Films @ ICM

Colors of Math

Film Directed by Ekaterina Eremenko

Colors of Math is an intellectually stimulating and beautifully shot film that invites us to look at mathematics from a new angle as the arena of the senses. To most people mathematics appears abstract, mysterious. Complicated. Inaccessible. But math is nothing but a language to express the world. Mathematics can be sensual. In this documentary, the beauty of mathematics, its sounds, colors, taste, and texture are revealed through the eyes of contemporary mathematical geniuses C´edric Villani, Aaditya V. Rangan, JeanMichel Bismut, G¨unter Ziegler, Maxim Kontsevich, and Anatoly Fomenko.

Source: University of Kentucky

 

12:30 PM – 12:50 PM 120-AB Short Communications

Generalization of the q-Mittag–Leffler Function and Its Applications in Fractional q-Calculus

  • DAYA LAL Suthar (Wollo University)
In this study, we employ the q-calculus framework to present a novel and more general form of the q-Mittag-Leffler function. We investigate numerous significant aspects of this function, including its image formula using the Kober fractional q-calculus operator, recurrence relations, convergence behavior, q-integral transforms, integral representations, and q-derivative formulae. A new five-parameter q-exponential function is also proposed, resulting in an expanded version of the generalized q-Mittag-Leffler function. In addition, we obtain q-integral representations and fractional q-derivatives of the Caputo and Hilfer types for this function. We solve the related q-fractional kinetic equations by employing the q-Laplace and q-Sumudu transforms based on Riemann-Liouville fractional q-calculus operators. Several unique and special situations are offered to highlight the utility of the primary findings. Finally, numerical demonstrations developed in MATLAB 16 corroborate the analytical conclusions by demonstrating the behavior of the proposed functions.
12:30 PM – 12:50 PM 115-C Short Communications

Inhomogeneous Diophantine Approximations: Some Recent Advances

  • Vasiliy Neckrasov (Brandeis University)
This talk is about the inhomogeneous Diophantine approximations, that is, approximations of pairs of a matrix and a vector (or, equivalently, approximations of systems of affine forms) from the metric point of view. There are three natural ways to treat this setup: we can just look at all pairs; we can fix the matrix (this is called "twisted approximations"), or we can fix some vector. In recent years, a lot has been done in the setup of pairs and fixed vector. However, many essential questions remained unanswered in the twisted case.We will give answers to some of these questions, build the metric theory of twisted approximations and observe some parallels between the twisted case and classical homogeneous Diophantine approximations. We will also see how twisted results serve as a bridge between the classical Khintchine-Groshev's theorem and zero-one law for Lebesgue measure of uniform approximations of pairs by Kleinbock and Wadleigh. Lastly, we will complement the aforementioned zero-one law by describing the sets of pairs uniformly approximable with arbitrary rates, and completely describe the Dirichlet spectra for this problem.This talk is based on preprints arXiv:2503.21180 (with Nikolay Moshchevitin), arXiv:2508.01912 and some work in progress.
12:30 PM – 12:50 PM 118-AB Short Communications

Lagrangian-Eulerian Formulations for Numerical Treatment of Hyperbolic Systems of Balance and Conservation Laws Several Dimensions on Cubical and Tetrahedral Meshes

  • Eduardo Abreu (Universidade Estadual de Campinas - Unicamp Brazil)
We present a construction and rigorous numerical analysis of Lagrangian-Eulerian schemes for effective computation of three-dimensional scalar (and systems of) hyperbolic conservation laws on structured cubical and tetrahedral meshes. We also provide several numerical 1D/Multi-D examples to verify the theory and discuss the capabilities of the novel approach, for instance, Compressible Euler flows with positivity of the density, the classical Orszag-Tang problem in magneto-hydrodynamics, which is well-known to satisfy the notable involution-constrained partial differential equation $\nabla \cdot B = 0$ (this condition is verified numerically by the proposed approach, i.e., without any imposition of an additional constraint in the formulation), and a nonstrictly hyperbolic three-phase flow system in porous media with a resonance point. We will also discuss high-performance computing of the new approach in a MPI environment and its performance via the typical strong scaling metric. We start by deriving fully-discrete and semi-discrete schemes for a generic three-dimensional hyperbolic conservation law, which is based on a novel concept of no-flow curves/surfaces/manifolds, which is effective for computational implementation: The first Lagrangian evolution step automatically handles the hyperbolic fluxes and, the second step, a Eulerian remap, which allows the use of a single structured cubical and tetrahedral mesh grid, thus eliminating the need for moving meshes while retaining local conservation. Due to the no-flow framework, there is no need to employ/compute the eigenvalues (exact or approximate values) - in fact there is no need to construct the relevant Jacobian of the hyperbolic flux functions, and thus giving rise to an effective and novel weak CFL-stability condition, which is effective for computing practice. The method is Riemann-solver-free and, hence, time-consuming field-by-field type decompositions are avoided in the case of multidimensional systems, for instance, the positivity of density for compressible Euler Flows and conservation laws with discontinuous space-time dependent flux functions, Orszag-Tang vortex system and a nonstrictly hyperbolic three-phase flow system (with a resonance point) and the 2D shallow water equations with variable topography and discontinuous data in a geometric intrinsic formulation. This scheme has also been successfully applied to nonlocal and balance hyperbolic problems.
12:30 PM – 1:30 PM Breaks

Lunch on Own

12:30 PM – 12:50 PM 115-A Short Communications

Mean Hausdorff Dimension: Properties, Applications and Conjectures

  • Jeovanny Muentes Acevedo (Universidad Tecnológica de Bolívar)
Consider the left shift $\sigma :([0,1]^{n})^{\mathbb{Z}}\rightarrow ([0,1]^{n})^{\mathbb{Z}}$. A problem in dynamical systems is decide if a system $(M,\phi)$ can be embedded in $\sigma$ (see [Lind00] and [LT2019]). The mean topological dimension of a dynamical system $(M,\phi)$, denoted by $\text{mdim}(M,\phi)$ (see [Gromov99]), is an invariant under topological conjugacy and an useful tool for this problem. Throughout several articles from Lindenstrauss, Weiss, Gutman, among others, it is proven that any minimal systems with a mean topological dimension less than $\frac{n}{2}$ can be embedded in  $\sigma$ (see [LT2019], and references therein). However, the mean topological dimension is difficult to calculate.In search of finding other ways to calculate the mean topological dimension, in 2019, Lindenstrauss and Tsukamoto ([LT2019]) introduced  the mean Hausdorff dimension of a dynamical system $\phi:M\rightarrow M$, where $M$ is a compact metric space with metric $d$, which we denote by   $\text{mdim}_{\text{H}}(M,d,\phi)$. The mean Hausdorff dimension is an upper bound for the mean topological dimension:  for any dynamical system $(M,\phi) $ we have that $$\text{mdim}(M,\phi)\leq \text{mdim}_{\text{H}}(M,d,\phi).$$In this talk, we will present the definition and important properties of the mean Hausdorff dimension, some interesting examples  and some conjectures (see [Muentes24A], [Muentes24B], Muentes24C], [Muentes24D]).   Bibliography[Acevedo24A]  J. Muentes,  A. Baraviera, A. Becker, E. Scopel. ``Metric mean dimension and mean Hausdorff dimension varying the metric.'' Qualitative Theory of Dyn. Sys.  (2024).[Muentes24B]  J. Muentes. ``Genericity of homeomorphisms with full mean Hausdorff dimension.'' Regular and Chaotic Dynamics (2024).[Muentes24C] J. Muentes, S. Romana. R. Arias. ``Density of the Level Sets of the Metric Mean Dimension for Homeomorphisms''. Journal of Dynamics and Differential Equations (2024).[Muentes24D] J. Muentes, S. Romana, R. Arias. ``H"older continuous maps on the interval with positive metric mean dimension.'' Revista Colombiana de Matematicas (2023).[Gromov99] M. Gromov. ``Topological invariants of dynamical systems and spaces of holomorphic maps: I.'' Math. Phy. Analysis and Geometry 2.4 (1999)[Lind00] E. Lindenstrauss, B. Weiss. ``Mean topological dimension." Israel Journal of Maths (2000)[LT2019] E. Lindenstrauss, M. Tsukamoto. ``Double variational principle for mean dimension (2019)
12:30 PM – 12:50 PM 115-B Short Communications

On Isometric Rigidity of Wasserstein Spaces

  • Tamás Titkos (Rényi Institute and Corvinus University)
In recent decades, there has been rapid development in the theory of optimal transport and its countless applications. One of the most important transport related metric structure is the so-called \(p\)-Wasserstein space \(\mathcal{W}_p(X)\), where \(X\) is a Polish metric space.A fundamental feature of \(p\)-Wasserstein spaces is that \(X\) embeds isometrically into \(\mathcal{W}_p(X)\), and every isometry of \(X\) induces an isometry of \(\mathcal{W}_p(X)\) via push-forward. Such isometries are called trivial. The space \(\mathcal{W}_p(X)\) is said to be isometrically rigid if all its isometries are trivial. This naturally raises the questions: do non-rigid Wasserstein spaces exist, and if so, what does a non-trivial isometry look like?In this talk, we survey what is currently known about isometries of \(p\)-Wasserstein spaces.The talk is based on joint works with Zoltán M. Balogh (Universität Bern, Bern), Gy. P. Gehér (Riverlane, Cambridge), G. Kiss (Corvinus University and HUN-REN Rényi Institute, Budapest), and Dániel Virosztek (HUN-REN Rényi Institute, Budapest.)
12:30 PM – 12:50 PM 118-C Short Communications

On the $\sigma_2$-curvature and volume of compact manifolds

  • Maria de Andrade

Inspired by the foundational work of Fischer and Marsden (1975) on scalar curvature deformations, we study the variational theory of the $\sigma_2$-curvature and its interplay with volume in compact Riemannian manifolds.

 

For closed manifolds, we characterize critical points of the total $\sigma_2$-curvature functional as $\sigma_2$-Einstein metrics. Building on results of Gursky–Viaclovsky and Hu–Li, we obtain a sharp necessary and sufficient condition for such a critical metric to be Einstein. Furthermore, we establish a volume comparison theorem for Einstein manifolds with respect to $\sigma_2$-curvature, showing that, under certain curvature conditions, the volume is controlled by $\sigma_2$.

 

For compact manifolds with non-empty boundary, we examine the volume functional restricted to metrics with constant $\sigma_2$-curvature and prescribed boundary metric. We characterize critical points via a boundary-value problem and prove that, in space forms, these critical points correspond precisely to geodesic balls. Finally, through a second-order analysis, we demonstrate that geodesic balls are local minima of the volume functional along a natural direction of variations.

 

This work systematizes and extends the deformation theory of higher-order curvatures and provides new geometric rigidity and comparison results related to $\sigma_2.$ 

 

This is part of a joint work with A. Silva Santos (UFS - Brazil) and T. Cruz (UFAL - Brazil).

12:30 PM – 12:50 PM 119-AB Short Communications

Optimal Radio $k$-Labelings of Graphs: Distance-Constrained Labelings

  • Devsi Bantva (Lukhdhirji Engineering College, Morbi-363642, Gujarat (India))
Let $G = (V,E)$ be a simple, finite, connected graph. A radio $k$-labeling of $G$ is a function $f : V(G) \rightarrow \{0,1,2,\ldots\}$ such that $|f(u)-f(v)| \geq k+1-d(u,v)$ holds for every pair of distinct vertices $u$ and $v$ of $G$, where $k$ is a positive integer and $d(u,v)$ denotes the distance between two vertices $u$ and $v$ in $G$. The span of a labeling function $f$ is defined as $span(f) = \max\{|f(u)-f(v)| : u,v \in V(G)\}$. The radio $k$-labeling number, denoted by $rn_k(G)$, is defined as $rn_k(G) := \min_{f}\{span(f)\}$, where the minimum taken over all radio $k$-labelings $f$ of $G$. A radio $k$-labeling $f$ of $G$ is called optimal if $span(f) = rn_k(G)$. This labeling problem is distance-constrained graph labeling as it assigns nonnegative integers (called colors or labels) to the vertices of $G$, with the assignment constrained by the distances between vertices. This graph labeling problem arises from the radio frequency assignment problem. The radio $k$-labeling problem generalizes several well-known graph labeling problems. For $k=1$, radio $1$-labeling is famous proper vertex coloring and $rn_1(G) = \chi(G)$. For $k=2$, radio $2$-labeling is distance two labeling and $rn_2(G) = \lambda(G)$. For $k=d-1$, where $d$ is the diameter of graph $G$, it is known as radio antipodal labeling, and $rn_{(d-1)}(G) = an(G)$, the radio antipodal number. Finally, for $k = d$, radio $d$-labeling is called radio labeling and $rn_d(G) = rn(G)$, the radio number. The radio $k$-labeling problem is considered one of the tough graph labeling problems, and the optimal labeling is investigated for very few graph classes. In this work, we discuss optimal distance two labeling and radio antipodal labeling of the Cartesian product of a tree and a complete graph. We determine the $\lambda$-number and the radio antipodal number for the Cartesian product of certain trees with a complete graph. We extend our study to radio labeling of graphs. We discuss optimal radio labeling of trees. We present an improved lower bound for the radio number of trees and a necessary and sufficient condition to achieve the lower bound. Using these results, we determined the radio number for several classes of trees. We discuss optimal radio labelings for the Cartesian product of trees with some other graphs. In summary, this work presents our recent progress on distance-constrained labelings, exploring both variations in the parameter $k$ and across different classes of graphs.
12:30 PM – 12:50 PM 116-A Short Communications

The Influence of Caputo Time Fractional Derivative on Wave Characteristics of Heat Conduction

  • Vinayak Kulkarni (University of Mumbai, India)
Fourier law (1807) assumes that the heat conduction process in a homogeneous medium, the heat flux vector and temperature gradient appears at the same time instant and consequently thermal signals propagate with an infinite speed. In order to achieve the finite speed of thermal wave, Cattaneo and Vernotte (1958) have reconstructed the Fourier law in terms of the thermal relaxation parameter. Furthermore, to study the lagging behaviour of the heat conduction, Tzou (1995) proposed the dual-phase-lag theory by introducing delay time translations in heat flux vector and in temperature gradient. The proposed model is an attempt to design a well-posed heat conduction equation considering non-Fourier effects in the context of Caputo time fractional derivative and study the influence of order of fractional derivatives along with phase lag parameter in the wave-like behaviour of heat conduction. The presence of relaxation time converts the corresponding heat conduction equation into a hyperbolic type that characterizes the combined diffusion and wave-like behaviour of heat conduction and predicts a finite speed of thermal wave propagation. The well posedness of the model has been proved mathematically by showing continuous dependence of the solution on the initial data and energy supply term. Moreover the existence and uniqueness of the solution have been proved subject to stability condition for the constitutive coefficients on the point spectrum. The analytical solutions of governing equations could be achieved by converting the original boundary value problem into an eigenvalue problem by the application of the Integral transforms. The convergence of infinite series solutions has been discussed using local integrability and bounded variation of the functions.The existing classical and non-classical theories of heat conduction have been recovered by considering the various special cases for the order of fractional derivatives and two different translations under consideration. The micro structural interactions and corresponding thermal changes have been studied due to the involvement of relaxation time and delay time translations. The non-local characteristics of fractional order parameters control the memory effects of temperature changes in the system. Consequently, presenting models could establish the scientific role of fractional order, phase-lags and the relaxation times to categorize the conducting materials in the mechanism of heat transfer.
12:50 PM – 1:10 PM 120-AB Short Communications

Boundedness of Pseudo-Differential Operators via Coupled Fractional Fourier Transform

  • Kanailal Mahato (Banaras Hindu University)
In this talk, we achieved significant outcomes regarding the coupled fractional Fourier transform and its kernel. We established pseudo-differential operators associated with the coupled fractional Fourier transform on Schwartz spaces, demonstrating that their composition results in another pseudo-differential operator. Additionally, we explored the composition of two pseudo-differential operators within Sobolev spaces and derived specific norm inequalities related to this. Furthermore, we successfully utilized some findings from the coupled fractional Fourier transform to examine the solutions of $n^{th}$-order linear non-homogeneous partial differential equations and wave equations. Finally, we provide examples that include graphs and tables to validate our theoretical results.
12:50 PM – 1:10 PM 119-AB Short Communications

Centrality in Connected Graphs via Convexity or Concavity

  • Kamal Lochan Patra (National Institute of Science Education and Research Bhubaneswar)
In graph theory, several central parts of graphs have been defined. The center, median and the security center are three such concepts defined for any connected graph, while others are specific to trees. These definitions typically involve a function defined on the vertex set of the graph. In this talk, we first generalize the concepts of convex and concave functions, originally defined for trees, to connected graphs. Using this, we provide a unified approach to prove the known results that each of the center, median, and security center of a connected graph is either a cut vertex or lies within a block. Additionally, we introduce three new central parts of a connected graph as generalizations of the subtree core, core vertices, and characteristic set of a tree, and examine their properties in relation to the center, median, and security center. We also show that for any graph $G$, there exists a supergraph $G'$ such that the subgraph induced by the characteristic center of $G'$ is isomorphic to $G$.This is a joint work with Dinesh Pandey.
12:50 PM – 1:10 PM 118-C Short Communications

Lifespan Estimates for Semilinear Damped Wave Equation in a Two-Dimensional Exterior Domain

  • YUTA WAKASUGI (Hiroshima University)
Lifespan estimates for semilinear damped wave equations of the form$\partial_t^2 u - \Delta u + \partial_t u = |u|^p$in a two dimensional exterior domain endowed with the Dirichlet boundary condition aredealt with. For the critical case of the semilinear heat equation $\partial_t v - \Delta v = v^2$ with theDirichlet boundary condition and the initial condition $v(0)=\varepsilon f$, the corresponding lifespancan be estimated from below and above by $\exp(\exp(C\varepsilon^{-1}))$ with different constants $C$. Thispaper clarifies that the same estimates hold even for the critical semilinear damped waveequation in the exterior of the unit ball under the restriction of radial symmetry. To achievethis result, a new technique to control $L^1$-type norm and a new Gagliardo--Nirenberg typeestimate with logarithmic weight are introduced.
12:50 PM – 1:10 PM 115-B Short Communications

New Local T1 Theorems for Bounded and Compact Singular Operators on Non-Homogeneous Spaces

  • Francisco Villarroya Alvarez (Santa Clara University)
We introduce new local $T1$ theorems to characterizeCalderon-Zygmund operators$$T(f)(x)=\int f(t)K(x,t)dt$$thatextend boundedly or compactly on $L^{p}(\mathbb R^{n},\mu)$, with $p\in (1,\infty )$ and $\mu $a measure of power growth.These operators are described by two properties: 1) an operator kernel $K$ whose generalized derivativedecays in the directions perpendicular and parallel to the diagonal, and 2) local testing conditions given by the $L^2(\mu)$-norm of the operator acting over the indicator functions of cubes when localized to their own support. The results, whose proofs do not require random grids, have weaker hypotheses than previously known local T1 theorems since they only require a countable collectionof testing functions. This is relevant for applications to singular integrals supported on fractal measures. As a corollary, we describe the measures $\mu$ of the complex plane for which the Cauchy integral defines a compact operator on $L^p(\mathbb C,\mu)$.
12:50 PM – 1:10 PM 118-AB Short Communications

On Some Recently Defined Metric Extensions, Their Properties and Applications

  • Inci Erhan (Aydin Adnan Menderes University)
The concept of distance, or more generally, metric, is a basic one in almost all sciences. The most commonly used metric is the usual distance in 3-dimensional Euclidean space. However, the research and developements in many different areas of science, engineering and technology require use of new types of distances(metrics) for various reasons: reducing the computational time and cost for the solutions of particular problems, providing the existence and uniqueness of their solutions in cases when the usual metrics do not apply, and others. Recently, the definition of the metric has been altered in different ways to give a new and more general form of a metric. Among the older ones can be mentioned the quasi-metric, b-metric, partial metric, G-metric, rectangular metric. Some of the more recent ones are the so-called suprametric, perturbed metric, interpolative metric, $\phi$-metric. The purpose of this talk is to present some of the most recent metric generalizations and give relations between them. In addition, we aim to introduce the use of these metrics in certain real life problems which illustrate the significance of the new metric types in connection with the solutions of these real life problems.
12:50 PM – 1:10 PM 116-A Short Communications

Ramifications of Temperature-Dependent Viscosity and Prandtl Number on MHD Forced Flow Over an Impermeable Symmetric Wedge

  • ESWARA ANNIGANAHALLY THAMMAIAH SETTY (GSSSIETW, Mysuru-570016, India)
The scientific and industrial use of fluids such as air, water, plasma, blood, ethanol, colloidal suspensions etc., is not possible without complete knowledge of their inherent and intricate thermo-physical transport properties. Under such circumstances, boundary layer theory plays a crucial role in understanding the convective heat transfer behavior between solid surface and flowing fluid. In a typical laminar flow, it is well-known that dynamic viscosity varies significantly with temperature. Moreover, Prandtl number which itself is a function of viscosity, varies with temperature too. Thus, the combined role of temperature-dependent viscosity and Prandtl number becomes an interesting physical phenomenon in fluid dynamics research.This research examines how temperature-dependent viscosity and Prandtl number affect the steady, MHD laminar forced flow of incompressible fluid (ethanol) over an impermeable wedge. Utilizing the similarity transformations, the governing coupled nonlinear partial differential equations are converted into system of coupled nonlinear ordinary equations and these flow equations tackled numerically, using the quasilinearized implicit finite-difference approach. The impact of temperature-dependent viscosity/Prandtl number on the local skin friction coefficient, Nusselt number, velocity and temperature fields is analyzed in the presence of a transverse magnetic field, for different wedge angles. The acquired results in the absence of certain key parameters are compared with previously reported works, and found to be in good agreement. The insights gained here are expected to provide a solid framework of accurate numerical calculations for the heat transfer community working on the thermal systems in industrial applications, including lubrication, transportation and food processing etc.
12:50 PM – 1:10 PM 115-A Short Communications

Sliding Dynamics and Invariant Manifolds of 3D Piecewise Linear Systems with Parallel Tangency Lines

  • Durval Jose Tonon (Federal University of Goias)
This paper investigates the sliding and crossing dynamics of three-dimensional piecewise linear systems with parallel tangency lines. A central goal is to characterize certain invariant manifolds, identifying them as limit cycles or invariant cylinders. In these systems, the sliding vector fields may generate a curve of pseudo-equilibria, indicating the occurrence of a bifurcation of higher codimension. Specifically, we consider systems of the form \(\dot{x} = A^{\pm}x + b^{\pm}\), assuming the tangency lines are parallel. For this class, we provide a detailed analysis of the sliding dynamics and present a bifurcation diagram with explicit conditions based on system parameters.The crossing dynamics are also thoroughly examined, and we establish precise parameter-dependent criteria for the existence of limit cycles, invariant cylinders, and scroll-wave-type behavior. Furthermore, we derive an upper bound for the number of crossing limit cycles. Several bifurcations are explored, including those involving homoclinic connections, as well as the emergence and disappearance of limit cycles.
1:10 PM – 1:30 PM 118-C Short Communications

Decay Rates for Navier-Stokes and Navier–Stokes–Coriolis Equations in Critical Sobolev Spaces

  • Gabriela Planas (Universidade Estadual de Campinas)
In this talk, I will present an algebraic upper bound on the decay rate of solutions to the Navier–Stokes and Navier–Stokes–Coriolis equations in critical spaces, obtained via the Fourier splitting method. The estimates are expressed in terms of the decay character of the initial data, yielding solutions that exhibit algebraic decay. The analysis highlights the distinct contributions of the linear and nonlinear components of the equations. The entire proof is conducted within the critical space framework. This represents the first application of the Fourier splitting method to establish decay bounds for a nonlinear equation in a critical space.
1:10 PM – 1:30 PM 120-AB Short Communications

Diagonal Process and Applications

  • Youssef Azouzi (University of Carthage)
We present a general diagonalization process for nets, which extends the classical Cantor diagonal argument for sequences. While the countable version is constructive, the general form is not. Several applications are provided in functional analysis, topology, and the theory of vector and Banach lattices. We also show that our result allows for a simplification of the proofs of several known theorems.
1:10 PM – 1:30 PM 115-B Short Communications

Fourier Inequalities in Variable Lebesgue Spaces

  • Matías Caruso (Instituto Balseiro)
Variable Lebesgue spaces were introduced by Orlicz in the 1930s and systematically studied by Nakano in the 1950s. During the last few years, they have gained great interest due to their applications to the modelling of electrorheological fluids and image processing.Many results that hold for classical Lebesgue spaces can be extended to the variable setting. However, a remarkable exception is the famous Hausdorff-Young inequality, that establishes that if $f \in L^p(\mathbb{R}^n)$, $1 \le p \le 2$, then\[\| \hat{f} \|_p \le C \| f \|_{p'},\]where $\hat{f}$ is the Fourier transform of $f$ and $p'$ is the conjugate exponent of $p$. This has motivated the consideration of extra ingredients in the search of the correct generalization of the inequality to the variable context, leading, for example, to weighted inequalities, inequalities with rearrangements or extra hypotheses.In this short communication, we provide different sufficient conditions and necessary conditions for the validity of Fourier inequalities in variable Lebesgue spaces.
1:10 PM – 1:30 PM 116-A Short Communications

Generalized Law of the Wake with Dip Phenomenon for Smooth Open-Channel Turbulent Flows: A Functional Equation Approach

  • SNEHASIS KUNDU (NATIONAL INSTITUTE OF TECHNOLOGY JAMSHEDPUR)
The mean velocity distribution over the whole flow depth in smooth open channel turbulent flow usually consists of three parts: (i) the logarithmic law in the overlap layer; (ii) the wake law in the outer region; and (iii) the boundary correction. This work presents a simple law, referred to as the generalized law of the wake, which combines all three hypotheses into a single equation. This law, unlike the log-wake law, does not explicitly contain the wake function and the boundary corrections, but shows this in its inherent nature. The equation is derived from a general functional equation with the hypothesis of a wake factor as the linear span of the velocity function at two points. The general functional equation reverts to the functional equation previously proposed by Guo(2023) for the overlap layer as a special case. The general solution of the functional equation is also discussed as the general solution of a delayed-differential equation. The model is validated over a widespread range of experimental and river field data, and satisfactory results are obtained. This law expresses the measured data well over the entire flow domain.ReferencesGuo, J. (2023). The log-law of the wall in the overlap from a functional equation, Journal of Engineering Mechanics 149(2): 06022005-1– 06022005-3.
1:10 PM – 1:30 PM 118-AB Short Communications

On a Boundary Value Problem with Integral and Multi-Point Boundary Conditions Associated with a Fractional $q$-difference Equation

  • Umit Aksoy (Atilim University)
In this study, a class of nonlinear $q$-difference equations of fractional order under multi-point and integral boundary conditions is studied. Green’s type functions are constructed with some of their properties and the representation of the solution of the linear equation with multi-point and integral conditions is obtained. The nonlinear boundary value problem is transformed into an integral equation and the fixed points of the related integral operator are investigated by using a contractive condition involving a comparison function. The Ulam-Hyers stability of the problem is also investigated. An example is provided to illustrate the main results.
1:10 PM – 1:30 PM 115-A Short Communications

Period Function in Planar Piecewise Hamiltonian Systems: Monotonicity and Critical Periods

  • Alex Carlucci Rezende (Universidade Federal de Sao Carlos)
We investigate the behavior of the period function in a family of planar piecewise Hamiltonian systems. Special attention is given to its monotonicity properties and the occurrence of critical periods. A complete bifurcation diagram is derived, highlighting parameter regions where the period function is strictly increasing or decreasing, as well as regions where it admits at most one simple critical period. The analysis is based on decomposing the period function into contributions from the underlying planar Hamiltonian systems on each side of the discontinuity line, which are then carefully combined to capture the global dynamics.
1:10 PM – 1:30 PM 119-AB Short Communications

Some Cohen-Macaulay Graphs Arising from Finite Commutative Rings

  • Ashitha Tom (Deva Matha College, Kuravilangad, Kottayam, Kerala, India-686633)
The investigation of Cohen-Macaulay rings holds a significant place in commutative algebra. These rings possess unique characteristics that have led to numerous applications in algebraic geometry. Consequently, distinguishing between Cohen-Macaulay and non-Cohen-Macaulay graphs is of considerable importance. Determining whether a given ring is Cohen-Macaulay is generally challenging, partly due to the constraints of symbolic computation. Thus, discovering alternative characterizations of Cohen-Macaulayness remains an intriguing problem.The construction of edge rings from graphs establishes a link between commutative algebra and graph theory. Let $G = (V, E)$ be a simple graph with $|V(G)| = n$. Consider the polynomial ring $S = \mathbb{K}[x_1, \ldots, x_n]$ in $n$ variables over a field $\mathbb{K}$. The squarefree quadratic monomial ideal associated with $G$ is given by \[I(G) = \big( x_i x_j \mid \{i,j\} \in E(G) \big) \]and is referred to as the \textit{edge ideal} of $G$. The quotient ring $\mathbb{K}[G] = S/I(G)$ is then known as the \textit{edge ring} of $G$. In 1990, Villareal demonstrated that if the edge ring $\mathbb{K}[G]$ is Cohen-Macaulay, then the graph $G$ is Cohen-Macaulay over $\mathbb{K}$.For a given commutative ring $R$, the total graph of $R$ is defined as a simple graph where the vertex set consists of elements of $R$, and two distinct vertices $x$ and $y$ are adjacent if their sum $x + y$ is a zero-divisor in $R$. This presentation aims to give a characterization of the Cohen-Macaulay total graph. Such a classification provides a broad family of Cohen-Macaulay and non-Cohen-Macaulay graphs, leading to an extensive class of edge rings that are Cohen-Macaulay.
1:10 PM – 1:30 PM 115-C Short Communications

The Possible Adelic Indices for Elliptic Curves Admitting a Rational Cyclic Isogeny

  • FNU Rakvi (The University of Maine)
In the 1970s, Serre proved that the adelic index of a non-CM elliptic curve over a number field is finite. More recently, Zywina conjectured the complete set of adelic indices for such curves over $\mathbb{Q}$. In this talk, we discuss a recent joint work with Kate Finnerty, Tyler Genao and Jacob Mayle in which we prove that Zywina's conjecture is true for the family of non-CM elliptic curves over $\mathbb{Q}$ that admit a nontrivial rational cyclic isogeny. This strengthens a result of Lemos that resolved Serre's uniformity question for the same family of curves.
1:30 PM – 1:50 PM 118-AB Short Communications

A Fixed Point Iterative Approach for Solving an Elastic Beam Equation

  • Faeem Ali (Aligarh Muslim University, Aligarh, India)
This paper applies a fixed-point iteration method to approximate the solution of a nonlinear elastic beam equation in a Banach space. The existence and uniqueness of the solution of the elastic beam equation are proved. Moreover, some convergence results are demonstrated for almost ϕ-contraction by the F$^*$- fixed point iteration method. Some illustrative numerical examples are formulated to validate our results. The results presented in this paper are new and extend, improve, and unify several relevant results in the literature.
1:30 PM – 1:50 PM 116-A Short Communications

Accelerating Cosmological Dynamics in f(Q) Gravity with Dynamical Stability Analysis

  • Rahul Vijay Bhagat (BITS-Pilani, Hyderabad Campus, Hyderabad)
In this study, we investigate the viability of the $f(Q)$ gravity model within the framework of symmetric teleparallel gravity as an alternative explanation for the late-time acceleration of the Universe. We reformulate the modified Friedmann equations into a system of coupled differential equations, ensuring that the minimal set of equations required for a second-order gravity theory is obtained. These equations are then solved numerically. To constrain the model parameters. we employ Bayesian inference using Markov Chain Monte Carlo (MCMC) techniques, incorporating different observational datasets. Our findings show strong consistency with observational data. The evolution of key cosmological parameters indicates that the model displays quintessence-like behavior at present, with a natural tendency to converge toward the $\Lambda$CDM model at late times. To further support this outcome, we perform a critical point analysis, which confirms the existence of a stable de Sitter attractor. The existence of a stable de Sitter attractor confirms the accelerating behavior of the model.
1:30 PM – 1:50 PM 120-AB Short Communications

Homotopies and Maps Between Eigenvalues of Some Generalized Lucas Sequences and the Mandelbrot Set

  • Arturo Ortiz-Tapia (Beaumont ISD)
The eigenvalues of companion matrices associated with generalized Lucas sequences, denoted as L, exhibit a striking geometric resemblance to the Mandelbrot set M. This work investigates this connection by analyzing the statistical distribution of eigenvalues and constructing a variety of homotopies that map different regions of L to structurally corresponding subsets of M.In particular, we explore both global and piecewise homotopies, including a sinusoidal interpolation targeting the main cardioid and localized deformations aligned with the periodic bulbs. We also study a variation of the Jungreis map to better capture angular and radial structures. In addition to visual and geometric matching, we classify the eigenvalues according to their dynamical behavior, identifying subsets associated with hyperbolic, parabolic, Misurewicz, and Siegel disk points.Our findings suggest that meaningful correspondences between L and M must integrate both geometric deformation and dynamical classification. In light of these observations, we also suggest a conjectural homeomorphism between L and a dense subset of the Mandelbrot cardioid boundary, based on the behavior of the sinusoidal homotopy and the eigenvalue accumulation.Finally, we prove that the sinusoidal homotopy defines a homeomorphism (modulo countable exceptions) from L onto the boundary of the Mandelbrot cardioid, and, when composed with Douady's tuning map, extends to any baby cardioid or stable region of M, reinforcing the structural correspondence between these sets.
1:30 PM – 2:30 PM Terrace Ballroom Special Plenary Lecture

Maestro Jean Pierre Serre

  • Peter Sarnak (Princeton University and IAS)
Since his spectacular arrival on the mathematical scene more than 75 years ago, Serre has impacted if not transformed all that he has touched. We give some concrete (and naturally biased) samples of his work.
1:30 PM – 1:50 PM 119-AB Short Communications

Moving and Stacking Squares for Greater Visibility

  • Milos Stojakovic (University of Novi Sad)
We consider unit square symbols that need to be placed at specified $y$-coordinates. Our hope is to optimize the drawing order of the symbols as well as their $x$-displacement, constrained within a rectangular container, to maximize the minimum visible perimeter over all squares. If the container has width and height at most $2$, there is a point that stabs all squares. In this case, we prove that a staircase layout is arbitrarily close to optimality and can be computed in $O(n\log n)$ time.If the width is at most $2$, there is a vertical line that stabs all squares, and in this case we give a 2-approximation algorithm (assuming fixed container height) that runs in $O(n\log n)$ time.As a minimum visible perimeter of 2 is always trivially achievable, we measure this approximation with respect to the visible perimeter exceeding 2. We show that, despite its simplicity, the algorithm gives asymptotically optimal results for certain instances.
1:30 PM – 1:50 PM 118-C Short Communications

Nonlinear Dynamical Behaviors, Asymmetric Complex Networks and Fractional Differential Calculus in Modeling and Analyzing Neurodegenerative Disorders and Memory Effects

  • Aziz Belmiloudi (Universite de Rennes, INSA Rennes, CNRS, IRMAR-UMR 6625, 35700 Rennes, France)
Modeling and analyzing nonlinear dynamical behaviors of complex systems in the framework of fractional-order calculus are becoming increasingly important. There are the basis for further predicting and controlling the complicated threads of most real-world systems (such as ecological, biological and physical systems). Time fractional dynamical models are particularly efficient, when compared to classical integer-order models, for describing the long memory and hereditary behaviors of many complex systems. In particular, they arise naturally in many biological phenomena such as neurobiology, cardiology and viscoelasticity with rich emergence phenomena, such as dynamical abrupt transitions, synchronization and spatiotemporal oscillations.In this work, we explain a few recent results concerning some phenomena which describe memory effects present in biological systems, particularly in the cardiac and cerebral systems. We start by giving an overview of the cardiac memory phenomenon, also termed Chatterjee phenomenon, and the memory effects in brain’s neural network : they can cause stability or synchronization problems, and give rise to highly complex behavior including oscillations and chaos. Next, in order to understand and effectively analyze various neurological activities and disorders in brain, we present a new mathematical brain connectivity model (and its mathematical analysis) which takes into account memory characteristics of neurons and their past history, the heterogeneity of brain tissue, and the local anisotropy of cell diffusion. For the connection structure between neurons, the graph theory, in which the discrete Laplacian matrix of communication graph plays a fundamental role, is considered. The main interest of this work is the investigation of dissipative dynamics and long-time behavior of the proposed fractional differential complex neural network model in asymmetrically coupled networks, and also of different Mittag--Leffler synchronization problems for such networked dynamical systems, when different types of interaction are simultaneously present. Finally, we provide conclusions and future perspectives. {\bf Keywords}: fractional-order dynamics; memory effects, graph Laplacian; asymmetric complex networks; complexmemristive neural networks; connected network on boundary; synchronization mechanism (with possible control), dissipativity; absorbing set; local anisotropy; cellular heterogeneity; spatio-temporal patterns
1:30 PM – 1:50 PM 115-C Short Communications

On Irrationality Criteria for Certain Constants

  • Suraj Singh Khurana (SRM University-AP)
We discuss a criterion for the irrationality of certain constants that arise from the Ramanujan summation of a family of infinite divergent sums. This work is motivated by a result of J. Sondow on the irrationality criterion for the Euler–Mascheroni constant.
1:30 PM – 1:50 PM 115-A Short Communications

On the Dynamics of Shift-Pseudoperiodic Functions

  • Gorachand Chakraborty (Sidho-Kanho-Birsha University)
In this work, we study the dynamics of a special typeof transcendental meromorphic functions called shift-pseudoperiodicfunctions. It is proven that the Fatou set of such functions is invari-ant under certain translations. We show that these functions cannever have Baker wandering domains. Some non-existence criteriaof Herman rings for such functions are given. A detailed discus-sion on completely invariant Fatou components is also provided.We further describe a class of shift-pseudoperiodic functions hav-ing wandering domains. Finally, a brief account of the dynamicsof semigroups generated by shift-pseudoperiodic entire functions ispresented.
1:30 PM – 1:50 PM 115-B Short Communications

Reverse Dynamic Hardy–Copson Type Inequalities on Time Scales for $0 < p < 1$

  • Zeynep Kayar (Van Yuzuncu Yil University)
This paper focuses on establishing nabla and delta dynamic inequalities on time scales for the parameter range $0 < p < 1$. In contrast to the classical dynamic Hardy–Copson inequalities derived for $p > 1$, the inequalities presented herein do not preserve the direction observed in the classical cases. Instead, owing to the exponent lying within the interval $(0, 1)$, the direction of the resulting inequalities is reversed. Furthermore, the derived inequalities are not only novel but also provide a unified framework for continuous and discrete cases, addressing the parameter range $0 < p < 1$ which has previously been unexplored.
3:00 PM – 3:45 PM 115-A Section Lecture

Automorphic Forms on Loop Groups and Explicit Constructions

  • Professor Yongchang Zhu (Tsinghua University and Beijing Institute of Mathematical Sciences and Applications)

This talk presents explicit constructions of automorphic forms on loop groups via the Weil representation and theta lifting. We review Eisenstein series on loop groups, including Garland's results and the entireness of cuspidal Eisenstein series. We then discuss the Weil representation of loop symplectic groups, the Siegel-Weil formula for loop groups, and the loop group generalization of the Rallis constant term formula for theta lifting, tower properties which yields a criterion for cuspidality and provides explicit cusp forms on loop groups. Finally, we present new explicit formulas for theta lifts from  SL(2) to  loop orthogonal groups and discuss their relation to Hecke eigenforms.

3:00 PM – 3:45 PM 120-AB Section Lecture

Classical Control of a Quantum System

  • Urmila Mahadev (California Institute of Technology)

In this talk, we'll discuss the connection between the problem of learning with errors (LWE) and quantum computation. LWE is a widely studied cryptographic assumption which is believed to be secure even for quantum computers, unlike assumptions that are commonly used today. We'll discuss how, even though LWE does not seem to have enough structure to be amenable to quantum algorithms, it does have enough structure to enable uniquely quantum functionality. We'll illustrate this by describing how the LWE assumption can be used to classically control a quantum system. 

3:00 PM – 3:45 PM 122-AB Section Lecture

Modularity Theorems for Abelian Surfaces

  • Toby Gee (Imperial College London)
An overview of my results with George Boxer, Frank Calegari and Vincent Pilloni on the modularity of abelian surfaces.
3:00 PM – 3:45 PM 116-A Section Lecture

Statistical Signal Detection in High Dimension

  • Song-Xi Chen (Tsinghua University)
This talk will review the development of high diemsnional statistical signal detection in the last three decades. It mainly focuses on the signals in the means of the underlying source populations with independent data, while extensions to covariance signals or temporal dependent data are also entertained. We are specifically interested in methods which are suitable for general data distributions beyond Gaussian. Properties of the more easily formulated \(L_2\) and \(L_{\infty}\) signal detection procedures are evaluated in terms of their control on the type I error probability and the power performance, and their limitation are also stated. To detect weak and sparse signals, several multi-thresholding tests that include the signature higher criticism test are discussed and compared in terms of their detection boundary and relative power performance. The performance of the \(L_2\), \(L_{\infty}\) and the multi-thresholding tests are evaluated with respect to different range of signal sparsity level under the special Gaussian distribution. A power enhancement formulation of the aforementioned tests can attain the best performance over the entire range of signal sparsity under Gaussianity.
3:00 PM – 3:45 PM 119-AB Section Lecture

Structural Stability in Moduli Spaces of Foliations on Complex Algebraic Surfaces

  • Bertrand Deroin (CNRS, Université de Cergy-Pontoise)
We report on certain results and open questions related to the dynamics of foliations on algebraic compact complex surfaces, with a particular emphasis on the geography of the stability/bifurcation loci in their moduli spaces.
3:00 PM – 3:45 PM 121-AB Section Lecture

Submanifolds in Contact Geometry

  • John Etnyre (Georgia Institute of Technology)
Studying submanifolds of contact manifolds has been a central part of the development of this vibrant subject. In this talk, I will survey what is known about such manifolds, the diverse tools one can use to study them, their impact on the general development of contact geometry, and current directions of research.
3:00 PM – 3:45 PM 118-C Section Lecture

Where Can Free Waves Concentrate?

  • Ruixiang Zhang (University of California, Berkeley)

Waves are ubiquitous in our daily life. Two best-known linear models are the free wave and free Schrödinger equations, whose simplest forms are very amenable to Fourier analysis. Still, a basic question—how large can a solution be, and where can it be large?—is surprisingly subtle and only partly understood, especially in higher dimensions. Over decades, it transpired that in order to answer this fundamental question, one often needs to understand whether and how much the solution can concentrate on important subsets of $\mathbb{R}^n$. I will discuss three kinds of such subsets (convex sets, semialgebraic sets and lattices) and their importance based on sample problems. Some of them have nice connections to nearby areas such as number theory, geometry and combinatorics.

3:30 PM – 4:30 PM Terrace Ballroom Public Lecture

Mathemalchemy: A Mathematical and Artistic Adventure

  • Ingrid Daubechies (Duke University)
Mathemalchemy is a collaborative art installation conceived as the brainchild of mathematician and physicist Ingrid Daubechies and fiber artist Dominique Ehrmann, and driven by the energy and enthusiasm of 24 mathematical artists and artistic mathematicians. The installation celebrates the creativity and beauty of mathematics. Playful constructs include a flurry of Koch snowflakes, Riemann basalt cliffs, and Lebesgue terraces. It was designed and constructed during the pandemic, and has been touring North America since January 2022; it will soon move to its 5th exhibition venue. The talk will review the genesis and creation of the installation, and highlight some of its mathematical features.
4:00 PM – 4:45 PM 122-AB Section Lecture

Automorphic Density Theorems and Applications

  • Valentin Blomer (University of Bonn)
An automorphic density theorem quantifies to what extent the Ramanujan conjecture may fail. We explain how trace formulae can establish density theorems in higher rank situations and present a panorama of arithmetic applications.
4:00 PM – 5:00 PM Benjamin Franklin Stage Receptions & Special Events

Behind the Scenes of Contours of American Mathematics: A Collaboration with the American Philosophical Society

  • Adrianna Link (American Philosophical society)
  • David Nelson (American Philosophical Society)

This talk will offer a behind-the-scenes look at the making of Contours of American Mathematics, a special exhibit exploring the history of 18th, 19th, and 20th century math as interpreted through the collections of the American Philosophical Society (APS) in Philadelphia. Curated by Karen Parshall (Commonwealth Professor of History and Mathematics, Emerita, at the University of Virginia) and created in collaboration with APS staff, the exhibit explores the mathematical contributions of figures including Benjamin Franklin, David Rittenhouse, Nathaniel Bowditch, James Joseph Sylvester, Emmy Noether, Mina Rees, and John von Neumann among many others. The presentation will highlight the curatorial process involved with creating both an in-person and digital exhibit and will include reflections on some of the challenges and opportunities involved with displaying a lesser-known aspect of the Society’s archives. By sharing this work with the ICM community, the presenters hope to increase the use of these collections by historians and mathematicians alike and offer a potential model for future collaborative projects.

4:00 PM – 4:45 PM 120-AB Section Lecture

Localization for Strongly Disordered Interacting Quantum Chains

  • Wojciech De Roeck (KU Leuven)
Anderson localization of a single quantum particle has been a topic in physics and mathematics since the seminal work of P. Anderson in 1958. In the last decades, the focus has shifted however to interacting particles. It was conjectured that some aspects of Anderson localization survive in macroscopic systems in the presence of interactions. In particular it is expected that the conductivity of strongly disordered quantum systems identically vanishes. In recent work with Lydia Giacomin, Francois Huveneers and Oskar Prosniak, we prove that this is indeed the case for one-dimensional systems, i.e. for chains.
4:00 PM – 4:45 PM 121-AB Section Lecture

Minimal Surfaces and Comparison Geometry

  • Otis Chodosh (Stanford University)
We discuss applications of area-minimization to the study of curvature in Riemannian geometry.
4:00 PM – 5:00 PM Hall E - Expo Poster Presentations

Poster Exhibition

"Pitchfork bifurcation and traveling waves for a planar ensemble of rigid filaments with repulsive interaction" by Gervy Marie Angeles (10 - Partial Differential Equations)

"On the existence of source-solutions to the multidimensional Burgers equation" by JOÃO FERNANDO DA CUNHA NARIYOSHI (10 - Partial Differential Equations)

"The nonlinear Schrödinger equation on metric graphs" by Damien Galant (10 - Partial Differential Equations)

"Traveling Band Solutions in Degenerate Chemotactic Systems: Existence, Stability, and Pattern Selection" by Isanka Hevage (10 - Partial Differential Equations)

"Minkowski-curvature equation under a Schwarzian constraint" by Kuo-Chih Hung (10 - Partial Differential Equations)

"Existence and Uniqueness of the Navier-Stokes Initial Value Problem in Infinite Space " by Kulyash Kaliyeva (10 - Partial Differential Equations)

"Initial-boundary value problems for Navier-Stokes-Voigt equations with power-law nonlinearity" by Khonatbek Khompysh (10 - Partial Differential Equations)

"Partially holomorphic solutions of higher order totally characteristic equations" by Jose Ernie Lope (10 - Partial Differential Equations)

"Effects of Stage-structure and Dispersal Mechanism on Species' Persistence" by Maria Amarakristi Onyido (10 - Partial Differential Equations)

"Global dynamics of solitons coupled to radiation for critical wave maps and nonlinear wave equations" by Mohandas Pillai (10 - Partial Differential Equations)

"New Analytical Soliton Solutions and Dynamical Analysis of a Double-Stranded DNA Model" by Md Nurul Raihen (10 - Partial Differential Equations)

"On Hardy Inequalities with Homogeneous Weights" by Subhajit Roy (10 - Partial Differential Equations)

"On the asymptotics of attractors of the Ginzburg-Landau complex equation in a perforated domain with an oscillating boundary: Supercritical case" by Altyn Toleubay (10 - Partial Differential Equations)

"Using Differential-Equation-Based Methods to Automate Microscopy Segmentation in Developmental Biology" by Markjoe Uba (10 - Partial Differential Equations)

"AI-Driven Data Augmentation and Sensitivity Analysis of Radiative Bödewadt Ternary Nanofluid Flow over a Porous Rotating Disk with Multiple Slips" by Shahirah Abu Bakar (11 - Mathematical Physics)

"Electrogravimagnetic Field of a Toroidal Resonator with Biquaternion Representation of Currents" by Bakhyt Alipova (11 - Mathematical Physics)

"On the Matrix Negative Order Korteweg-de Vries Equation - the Commutative Case" by Aygul Babadjanova (11 - Mathematical Physics)

"Transport Boundary Value Problems for the Klein-Gordon Equation and Their Solution " by Aigulim Bayegizova (11 - Mathematical Physics)

"Mixed Physical Informed Neural Networks in Bio-Fluid Mechanics: Ureter Applications" by Kh Mekheimer (11 - Mathematical Physics)

"Enhancing Heat Transfer Using GO–MoS₂/Glycerine Hybrid Nanofluid under Slip Conditions on a Riga Plate" by Nor Ain Azeany Mohd Nasir (11 - Mathematical Physics)

"Magnetohydrodynamics Ternary Hybrid Nanofluid Flow Over a Permeable Moving Surface" by Nur Syahirah Wahid (11 - Mathematical Physics)

"Coordinate-Wise Elephant Random Walk" by Denisse Escobar Parra (12 - Probability)

"Stability Criteria for Rough Systems" by Thanh Hong Phan (12 - Probability)

"Boundary Value Problem with Parameter for Impulsive Integro-Differential Equation under Integral Constraints" by Elmira Bakirova (14 - Mathematics of Computer Science)

"Bit Complexity of Polynomial GCD on Sparse Representation" by Xiaoshan Gao (14 - Mathematics of Computer Science)

"Evolutionary Game Theory (EGT) Provides a Rigorous Mathematical Paradigm for Automating Optimal Large Language Model (LLM) Selection" by Prasad Kothari (14 - Mathematics of Computer Science)

"Detection of Malicious Images Generated by Large Language Models Using Graph Neural Networks and Feature-Based Representations" by Mohammed Serrhini (14 - Mathematics of Computer Science)

"Multivariate Information Measures: A Copula-Based Approach" by Mohd Arshad (17 - Statistics, Machine Learning, Image and Signal Processing)

"Image Encryption Based On Newly Designed Chaotic Map" by Kritika Gupta (17 - Statistics, Machine Learning, Image and Signal Processing)

"Predictive Models for Breast Cancer Brain Metastasis: An Integration of Neuroimaging and Genomics Data for Better Clinical Practice" by Chipo Zidana (17 - Statistics, Machine Learning, Image and Signal Processing)

4:00 PM – 5:00 PM Hall E - Expo Poster Presentations

Poster Presentation by Author

"Pitchfork bifurcation and traveling waves for a planar ensemble of rigid filaments with repulsive interaction" by Gervy Marie Angeles (10 - Partial Differential Equations)

"On the existence of source-solutions to the multidimensional Burgers equation" by JOÃO FERNANDO DA CUNHA NARIYOSHI (10 - Partial Differential Equations)

"The nonlinear Schrödinger equation on metric graphs" by Damien Galant (10 - Partial Differential Equations)

"Traveling Band Solutions in Degenerate Chemotactic Systems: Existence, Stability, and Pattern Selection" by Isanka Hevage (10 - Partial Differential Equations)

"Minkowski-curvature equation under a Schwarzian constraint" by Kuo-Chih Hung (10 - Partial Differential Equations)

"Existence and Uniqueness of the Navier-Stokes Initial Value Problem in Infinite Space " by Kulyash Kaliyeva (10 - Partial Differential Equations)

"Initial-boundary value problems for Navier-Stokes-Voigt equations with power-law nonlinearity" by Khonatbek Khompysh (10 - Partial Differential Equations)

"Partially holomorphic solutions of higher order totally characteristic equations" by Jose Ernie Lope (10 - Partial Differential Equations)

"Effects of Stage-structure and Dispersal Mechanism on Species' Persistence" by Maria Amarakristi Onyido (10 - Partial Differential Equations)

"Global dynamics of solitons coupled to radiation for critical wave maps and nonlinear wave equations" by Mohandas Pillai (10 - Partial Differential Equations)

"New Analytical Soliton Solutions and Dynamical Analysis of a Double-Stranded DNA Model" by Md Nurul Raihen (10 - Partial Differential Equations)

"On Hardy Inequalities with Homogeneous Weights" by Subhajit Roy (10 - Partial Differential Equations)

"On the asymptotics of attractors of the Ginzburg-Landau complex equation in a perforated domain with an oscillating boundary: Supercritical case" by Altyn Toleubay (10 - Partial Differential Equations)

"Using Differential-Equation-Based Methods to Automate Microscopy Segmentation in Developmental Biology" by Markjoe Uba (10 - Partial Differential Equations)

"AI-Driven Data Augmentation and Sensitivity Analysis of Radiative Bödewadt Ternary Nanofluid Flow over a Porous Rotating Disk with Multiple Slips" by Shahirah Abu Bakar (11 - Mathematical Physics)

"Electrogravimagnetic Field of a Toroidal Resonator with Biquaternion Representation of Currents" by Bakhyt Alipova (11 - Mathematical Physics)

"On the Matrix Negative Order Korteweg-de Vries Equation - the Commutative Case" by Aygul Babadjanova (11 - Mathematical Physics)

"Transport Boundary Value Problems for the Klein-Gordon Equation and Their Solution " by Aigulim Bayegizova (11 - Mathematical Physics)

"Mixed Physical Informed Neural Networks in Bio-Fluid Mechanics: Ureter Applications" by Kh Mekheimer (11 - Mathematical Physics)

"Enhancing Heat Transfer Using GO–MoS₂/Glycerine Hybrid Nanofluid under Slip Conditions on a Riga Plate" by Nor Ain Azeany Mohd Nasir (11 - Mathematical Physics)

"Magnetohydrodynamics Ternary Hybrid Nanofluid Flow Over a Permeable Moving Surface" by Nur Syahirah Wahid (11 - Mathematical Physics)

"Coordinate-Wise Elephant Random Walk" by Denisse Escobar Parra (12 - Probability)

"Stability Criteria for Rough Systems" by Thanh Hong Phan (12 - Probability)

"Boundary Value Problem with Parameter for Impulsive Integro-Differential Equation under Integral Constraints" by Elmira Bakirova (14 - Mathematics of Computer Science)

"Bit Complexity of Polynomial GCD on Sparse Representation" by Xiaoshan Gao (14 - Mathematics of Computer Science)

"Evolutionary Game Theory (EGT) Provides a Rigorous Mathematical Paradigm for Automating Optimal Large Language Model (LLM) Selection" by Prasad Kothari (14 - Mathematics of Computer Science)

"Detection of Malicious Images Generated by Large Language Models Using Graph Neural Networks and Feature-Based Representations" by Mohammed Serrhini (14 - Mathematics of Computer Science)

"Multivariate Information Measures: A Copula-Based Approach" by Mohd Arshad (17 - Statistics, Machine Learning, Image and Signal Processing)

"Image Encryption Based On Newly Designed Chaotic Map" by Kritika Gupta (17 - Statistics, Machine Learning, Image and Signal Processing)

"Predictive Models for Breast Cancer Brain Metastasis: An Integration of Neuroimaging and Genomics Data for Better Clinical Practice" by Chipo Zidana (17 - Statistics, Machine Learning, Image and Signal Processing)

4:00 PM – 4:45 PM 119-AB Section Lecture

Some Recent Developments in Structural Ergodic Theory

  • Tim Austin (Warwick University)
In classical ergodic theory, a handful of major results connect the Kolmogorov--Sinai entropy of a measure-preserving transformation to its structural properties. These properties include the existence of generating observables (as in Krieger's theorem) and factor maps or isomorphisms to Bernoulli shifts (as in Sinai's and Ornstein's theorems).Over the last twenty years, related research for measure-preserving actions of other countable groups has started to come into its own. Beginning with the new notions of `Rokhlin' and `sofic' entropy, some of the older structure theory has been generalized. But new phenomena have also come into view, and some foundational questions remain open.This talk will survey a few recent advances and remaining open questions in this area.
4:00 PM – 4:45 PM 118-C Special Section Lecture

The Kakeya Set Conjecture in R^3

  • Joshua Zahl (Chern Institute of Mathematics, Nankai University)
A Besicovitch set is a compact subset of Rn that contains a unit line segment pointing in every direction. The Kakeya set conjecture asserts that every Besicovitch set in Rn has Minkowski and Hausdorff dimension n. I will discuss progress on this conjecture, leading to the resolution of the Kakeya set conjecture in three dimensions. This is joint work with Hong Wang.
4:45 PM – 5:30 PM 117-A IMU Panel

IMU Commission on Developing Countries Poster Session: Mathematical Collaboration in the Global South and Creating Opportunities

4:45 PM – 7:15 PM 116-A IMU Panel

IMU Commission on Developing Countries: Mathematical Collaboration in the Global South and Creating Opportunities

  • Andrea Solotar (IMU)
  • Anjana Pokharel (Tribhuvan University)
  • Diaraf Seck (AMU)
  • Hiraku Nakajima (International Mathematical Union)
  • Jacqueline Godoy Mesquita (UMALCA)
  • Jose Emie C. Lope (SEAMS)
  • Ludovic Rifford (IMU)
  • Mariel Saez Trumper (IMU)
  • Pascel Hubert (CIRM)
  • Yuri Tschinkel (Simons Foundation)

Moderators:

  • Ludovic Rifford
  • Mariel Saez Trumper

Panelists:

  • Andrea Solotar
  • Angel Pineda
  • Anjana Pokharel
  • Claudia Lederman
  • Diaraf Seck
  • Hiraku Nakajima
  • Jacqueline Godoy Mesquita 
  • Jose Emie C. Lope
  • Pascel Hubert
  • Victor Amarachi Uzor

 

5:00 PM – 5:45 PM 118-C Section Lecture

Dynamics of Ideal Fluid Flows

  • Tarek Elgindi (Duke University)

Ideal fluid flows are dynamical rearrangements of space that minimize kinetic energy. Such flows, which solve the Euler equations, exhibit a wide range of interesting phenomena. We will give an overview of many of these phenomena, which have been rigorously established by many authors in recent years, and then focus mainly on questions related to steady solutions and finite-time singularities.

5:00 PM – 5:45 PM 119-AB Section Lecture

Entropy Methods in Combinatorics

  • Wojciech Samotij (Tel Aviv University)
Even though entropy methods have been used in combinatorics for at least five decades, only in recent years has their use really proliferated. There are now tens, if not hundreds, of combinatorial papers that crucially rely on the notion of entropy and exploit the various powerful identities and inequalities relating entropies. We attempt to give a broad overview of these works, outlining some of the key ideas.
5:00 PM – 5:45 PM 120-AB Section Lecture

Spectral Statistics of Sparse Random Graphs

  • Jiaoyang Huang (University of Pennsylvania)

We survey recent progress on the spectral statistics of sparse random graphs, with an emphasis on the Erdős–Rényi model and random ddd-regular graphs. The adjacency matrices of sparse random graphs form a canonical random matrix ensemble characterized by sparsity and, in some cases, dependent entries: most entries are zero, while degree constraints can induce long-range correlations absent from classical Wigner models. We discuss universality results for eigenvalue statistics in the bulk and at the spectral edge, as well as for eigenvectors. In the fixed-degree regime, edge universality for random d-regular graphs implies that asymptotically about 69% of d-regular graphs are Ramanujan.


 

5:00 PM – 5:45 PM 121-AB Section Lecture

Structural Approaches to Fukaya Categories and Mirror Symmetry

  • Sheel Ganatra (University of Southern California)
We survey some recent and in-progress structural and geometric tools for computing Fukaya categories of Liouville and Weinstein sectors and distinguished subcategories within them. Then we describe some applications and desired goals of this framework, including within mirror symmetry.
5:00 PM – 5:45 PM 122-AB Section Lecture

Unramified Automorphic Forms

  • Sam Raskin (Yale University)
We will discuss recent progress on understanding everywhere unramified automorphic forms over function fields. The main application, joint with D. Gaitsgory and V. Lafforgue, is a proof of the Arthur-Ramanujan conjecture in this setting, , which describes the magnitudes of Hecke eigenvalues of cusp forms. This is ultimately obtained as a consequence of the geometric Langlands conjecture for D-modules in characteristic 0. In this talk, we will give an introduction to this circle of ideas.
6:00 PM – 6:45 PM 119-AB Special Section Lecture

Channel Polarization and Polar Codes

  • Erdal Arikan (Bilkent University)
Polar codes provide the first explicit family of low-complexity codes that provably achieve the capacity of any binary-input memoryless symmetric (BMS) channel under successive-cancellation (SC) decoding. The key idea is channel polarization: by applying a simple binary linear transform to independent copies of a BMS channel recursively, one synthesizes a large set of BMS channels that become either almost noiseless or almost pure noise, with the fraction of good channels approaching the capacity. A polar code is formed by placing information on good indices and freezing the rest; SC decodes bits in sequence using the corresponding synthetic channels. Encoding and SC decoding admit quasi-linear time and linear space complexity. The result is a capacity-achieving, structurally simple coding framework with practical implementations and broad generalizations.
6:00 PM – 6:45 PM 120-AB Section Lecture

Energy Lagrangian Flows for Singular SPDEs and Applications

  • Nicolas Perkowski (Freie Universität Berlin)

Energy Lagrangian flows are a formulation of the Lagrangian flows of Di Perna-Lions and their stochastic counterparts by Le Bris-Lions and Figalli in the setting of singular stochastic dynamics, partly in regimes where classical and pathwise theories break down. A key notion is "probabilistic subcriticality": even for scaling critical or supercritical equations, regularity of the law combined with coercivity of the generator may yield existence and uniqueness. I will outline the construction and well-posedness results, the relation to pathwise constructions, and applications to hydrodynamics and numerical analysis.

6:00 PM – 6:45 PM 121-AB Section Lecture

Graphs and Diffeomorphisms

  • Tadayuki Watanabe (Department of Mathematics, Kyoto University)
I explain that the rational homotopy type of the group of diffeomorphisms of the \(d\)-disk, \(d\geq 4\), or of some manifold may include a huge combinatorial structure coming from Kontsevich's graph complex or its variant.
6:00 PM – 6:45 PM 118-C Section Lecture

Long-Term Behavior of Linear and Nonlinear Waves

  • Sung-Jin Oh (University of California, Berkeley)
In this talk, I will survey recent progress on the long-term behavior of solutions to linear and nonlinear hyperbolic equations, with a focus on robust physical space techniques. I will describe a general method (joint work with J. Luk) for determining the leading-order late-time tails for wave equations in odd spatial dimensions, which is applicable to nonlinear problems on dynamical backgrounds, and further developments of this method. Also, I will discuss a new physical space approach for establishing the global asymptotics of the variable-coefficient Klein--Gordon equation (joint work with F. Pasqualotto and N. Tang). Throughout, the emphasis will be on methods that are applicable to problems with variable coefficients and nonlinearities, such as those arising in the study of waves on black hole spacetimes or interacting with solitons.
6:00 PM – 6:45 PM 122-AB Section Lecture

Rationality of Hypersurfaces

  • Stefan Schreieder (Leibniz University Hannover)
A classical question in algebraic geometry is to determine which varieties, and in particular, which hypersurfaces, are rational or at least satisfy one of the weaker notions such as unirationality, retract rationality or stable rationality. This essentially amounts to asking whether (almost) all solutions of a given polynomial equation can be parametrized by rational functions. It is therefore a basic question about the solvability of polynomial equations. In this talk, I will present some results and open questions in this area. The techniques used range from algebraic cycles, quadratic forms and unramified cohomology to combinatorics and regular matroids. Some of the results presented will be based on joint work with J. Lange and on joint work with P. Engel and O. de Gaay Fortman.
7:00 PM – 8:30 PM Michael A. Nutter Theater Art & Music @ ICM

The American Mathematical Society Presents: The Music of Mathematics

  • Dmitri Tymoczko (Princeton University)

The American Mathematical Society presents a hybrid lecture and performance exploring the many beautiful connections between mathematics and music, featuring lead musician Dmitri Tymoczko. The general public will be invited to enjoy an opportunity to experience mathematics from a different perspective. Please RSVP to attend this special performance.

Open to all ICM attendees

7:15 PM – 8:15 PM Terrace Ballroom Abel Lecture

Abel Lecture: Submodular Functions, Limits, and Bubbles

  • László Lovász (Alfréd Rényi Institute of Mathematics)

László Lovász is giving this Abel Lecture.

In the last 20 years, limit theories of sequences of large discrete structures (graphs, permutations, posets) have been developed. Finite graphs have associated matroids, and it is a natural task to describe what sort of convergence and limit objects for these matroids are implied by the convergence of a graph sequence. Matroids, introduced by Whitney in 1935, and more generally submodular setfunctions, provide common generalizations and transparent proofs of many combinatorial results in graph connectivity, flow theory, matching theory, the theory of rigidity of rameworks, and many other topics. To define appropriate limit objects, submodular setfunctions on infinite sets, in particular sigma-algebras, have to be considered. Such setfunctions are also important in analysis, going back to the seminal work of Choquet (1954) in the theory of electric capacity and the ``nonlinear integral''. These two research lines, however, have not had much interaction. The goal of the research surveyed in this paper is to describe meaningful analogies between important notions and results for finite matroids and submodular setfunctions on sigma-algebras, and to develop a limit theory for submodular setfunctions.

Wednesday, July 29, 2026

9:00 AM – 4:00 PM Hall E - Expo Expo and Collaborations

Exhibition & Collaboration

9:00 AM – 10:00 AM Terrace Ballroom Plenary Lecture

Recent Results in Ramsey Theory

  • Robert Morris (IMPA)

In combinatorics, one is often presented with a large "unstructured" object, and asked to find a smaller "structured" object inside it. One of the earliest and most influential examples of this phenomenon was the theorem of Ramsey, proved in 1930, which states that if n = n(k) is large enough, then in any red-blue colouring of the edges of the complete graph on n vertices, there exists a monochromatic clique with k vertices.  

Over the past few years there have been a series of remarkable breakthroughs related to Ramsey's theorem. In this talk we will first give a gentle introduction to the area, and then discuss a few of these, including an exponential improvement for the diagonal Ramsey numbers, and some amazing new constructions for off-diagonal Ramsey numbers.

10:15 AM – 11:15 AM Terrace Ballroom Plenary Lecture

Singularity Models in 3D Ricci Flow

  • Simon Brendle (Columbia University)
Since its introduction by Richard Hamilton in 1982, the Ricci flow has become a fundamental tool in geometry and topology. From the point of view of PDE, the Ricci flow is a system of nonlinear parabolic equations. It can be viewed as the heat equation analogue of the Einstein equations in general relativity. The central problem is to understand singularity formation. In other words, what does the geometry look like at points where the curvature is large? In a spectacular breakthrough in 2002, Perelman achieved a qualitative understanding of singularity formation in dimension 3; this is sufficient for topological conclusions. In this lecture, we will discuss more recent developments which have led to a complete classification of singularity models in dimension 3.
10:30 AM – 10:50 AM 116-A Short Communications

Comprehensive analysis of deterministic and stochastic eco-epidemic models incorporating fear, refuge, supplementary resources, and selective predation effects.

  • Samares Pal

In this investigation, we delve into the dynamics of an ecoepidemic model, considering the intertwined influences of fear, refuge seeking behavior, and alternative food sources for predators with selective predation. We extend our model to incorporate the impact of fluctuating environmental noise on system dynamics. Through simulations, we unveil the stabilizing effect of the fear factor on susceptible prey reproduction, juxtaposed against the destabilizing roles of prey refuge behavior and disease prevalence intensity. Notably, when disease prevalence intensity is too low, the infection can be eradicated from the ecosystem. Our deterministic analysis reveals a complex interplay of factors: the system destabilizes initially but then stabilizes as the fear factor suppressing disease prevalence intensifies, or as predators exhibit a stronger preference for infected prey over susceptible ones, or as predators are provided with more alternative food sources. Observationally, we note that in system subjected to stochasticity, oscillations tend to cluster around the coexistence equilibrium of the corresponding deterministic model when white noise intensity is low. However, with increasing white noise intensity, oscillation amplitudes escalate. Critically, very high levels of white noise can lead to the eradication of infection from the ecosystem.

10:30 AM – 10:50 AM 116-A

Comprehensive analysis of deterministic and stochastic eco-epidemic models incorporating fear, refuge, supplementary resources, and selective predation effects.

10:30 AM – 10:50 AM 115-B Short Communications

Cubic Oscillator : Geometric Approach and Zeros of Eigen-Functions.

  • Faouzi Thabet (Institut Supérieur d'Informatique de Medenine)
A big challenge in the asymptotic theory of $\mathcal{ODE}$ in complex domains(on a Riemann surface more generally) is to study Stokes graphs mutationsunder changes of parameters in a data space $\mathcal{D}.$ In this talk, wetreat the cubic polynomial case. We give a geometric approach to the cubicoscillator ($C.O$) with three distinct turning points based on $\mathcal{D}%/\mathcal{SG}$\ correspondence. The existence of quantization conditions,depending on extra data in the potential is related to some particularcritical graphs of the quadratic differential $A\left( z-a\right) \left(z^{2}-1\right) dz^{2},$ where $A$ is a non vanishing complex number, and$a\in%%TCIMACRO{\U{2102} }%%BeginExpansion\mathbb{C}%EndExpansion\setminus\left\{ -1,1\right\} .$ We investigate this geometric approach intwo levels : the first level is the study of an inverse spectral problemrelated to the ($C.O$), while the second level is devoted to the descriptionof the zeros locations of eigen-functions related to this oscillator. Ourresults may be considered as a positive answer to a conjecture due to C.M.Bender \& al in the case of ($C.O$).
10:30 AM – 10:50 AM 115-C Short Communications

On Two Variable Artin's Conjecture

  • Suhita Hazra (Chennai Mathematical Institute)
In 1927, during a conversation with H. Hasse, E. Artin posed the following conjecture:If $a$ is neither $-1$ nor a perfect square then $a$ is primitive root for infinitely many primes.Moreover he conjectured the asymptotic density of such primes. Though many significant partial results are known in this direction, yet we do not know a single integer $a$, for which the conjecture holds. A variant of this conjecture, known as the two variable Artin's conjecture, introduced by Moree and Stevenhagen in 2000 asks about the size of the set $$\{ p \leq x ~:~ p \text{ prime, } \phantom{m} a \bmod p \in \langle b \bmod p \rangle \}$$ for any two multiplicatively independent elements $a$ and $b$ in $\mathbb{Q}^*$. In this talk, we would like to present a recent work with M. Ram Murty and Jyothsnaa Sivaraman where we improve the unconditional lower bound of the above set given by Murty-Seguin-Stewart.
10:30 AM – 10:50 AM 115-A Short Communications

Quantitative and Qualitative Results on Distance Sets in Large Fractal-Type Sets

  • Senthil Raani Kalirathnam Srinivasagam (IISER Berhampur)
In this talk, we synthesize two recent advances in distance-set theory. We briefly see an improved threshold for the Falconer pinned-distance conjecture in higher dimensions by Du, Ou, Ren & Zhang, and then the quantitative structure of distance sets in sparse but large‐dimension sets obtained in the work joint with Malabika Pramanik. Together, these results offer both qualitative and quantitative analysis of distance sets. To study the quantitative structure of the distance sets we explore how “large” Borel sets in d-dimensional Euclidean space $\mathbb R^d$, even those of Hausdorff dimension near $d$ but not full measure, produce rich distance sets containing explicit unions of intervals, with lengths governed by density‐rich subcubes, yielding a quantitative Mattila–Sjölin theorem. Further, we discuss the characterizations of the sets that admit all sufficiently large distances and discuss the structure of the distance sets of quasi-regular sets. We end with applications of techniques to quantify other patterns, such as k-chains, finite trees in thin sets and potential problems of distance sets in Heisenberg group.
10:50 AM – 11:10 AM 115-C Short Communications

Irrationality of Zeros of Polygamma Functions

  • preeti preeti (Chennai Mathematical Institute)
Our work owes its origin to a recent note of Ram Murty in which he proved that all the zeros of the digamma function are irrational with at most one possible exception. We extend this investigation to higher-order polygamma functions.
10:50 AM – 11:10 AM 115-A Short Communications

Mathematical Modelling of Nonlinear Waves

  • Angela Slavova (Institute of Mechanics, Bulgarian Academy of Sciences)
The study of water waves involves various disciplines such as mathematics, physics and engineering and within this there are many specific areas of direct or associated interest such as pure mathematics, applied mathematics, modelling, numerical simulation, laboratory experiments, data collection in the field, the design and construction of ships, harbours, the prediction of natural disasters, climate studies and so on. In this lecture we shall present travelling wave solutions of shallow water waves. Camassa-Holm considered a third order nonlinear PDE of two variables modelling the propagation of unidirectional irrotational shallow water waves over a flat bed, as well as water waves moving over an underlying shear flow. In the special case of the motion of a shallow water over a flat bottom the corresponding system was simplified by Green and Naghdi and related to an appropriate two component first order Camassa-Holm system. Another interesting system of nonlinear PDE is the viscoelastic generalization of Burger's equation. In the above mentioned systems we are looking for travelling wave solutions and we are studying their profiles. To do this we use several results from the classical Analysis of ODE that enable us to give the geometrical picture and in several cases to express the solutions by the inverse of Legendre's elliptic functions. As an application we shall present propagation of tsunami waves from their small disturbance at the sea level to the size they reach approaching the coast. Even with the aid of the most advanced computers it is not possible to find the exact solutions to the nonlinear governing equations for water waves. For this purpose we introduce Cellular Nonlinear Network (CNN) approach.
10:50 AM – 11:10 AM 115-B Short Communications

Modifying the Field Axioms to Create Infinite and Infinitesimal Real Numbers

  • Brendan Santangelo (Stockton University)
By modifying three of the field axioms and including two other axioms, it is possible to create extensions to fields using the equivalence classes of equivalence relations. If that field is the field of real numbers, then an ordering can be placed on these extensions. As a result, we get what can be called infinite and infinitesimal real numbers. An introduction and analysis of these extensions is conducted concluding with the creation of infinite and infinitesimal real numbers. And in hope of justifying their names, a quick discussion comparing these numbers to other known infinite and infinitesimal numbers is conducted.
10:50 AM – 11:10 AM 116-A Short Communications

On the Local Convergence of a Two-Step Combined Newton-Secant-Kurchatov Type Method Under Two Different Continuity Conditions

  • Jai Prakash Jaiswal (Guru Ghasidas Vishwavidyalaya ( A Central University), Bilaspur (CG)-495009, India)
In this paper, we explore a double-step method for solving nonlinear equations containing a differentiable and non-differentiable operator. Our approach is built upon the combination of three different methods. We have analyzed the local convergence of the suggested method, considering both Lipschitz and L-average conditions \& established the superquadratic ($\approx 2.414$) order of convergence. Finally we have pictured a comparison of the numerical results in comparison with several existing methods.
11:10 AM – 11:30 AM 116-A Short Communications

Attention-Based Physics-Informed Neural Network for Solving Time-Fractional Black-Scholes Equations

  • Neha Yadav (Dr. B.R. Ambedkar NIT Jalandhar)
This work presents a novel Physics-Informed Neural Networks (PINNs) framework augmented with an attention mechanism to solve time-fractional Black-Scholes partial differential equations - a challenging class of equations characterized by the nonlocality of fractional derivatives. Conventional numerical methods often encounter difficulties in discretization and suffer from high computational costs when addressing such problems. To overcome these limitations, our hybrid approach integrates the L1 finite difference scheme for approximating fractional derivatives with automatic differentiation for integer-order terms, facilitating end-to-end learning of both market dynamics and fractional behaviors without reliance on traditional grid-based solvers.To enhance convergence and adaptability, an attention mechanism is incorporated combined with a novel adaptive weighting strategy. This results in improved learning stability and predictive accuracy, outperforming existing attention-based PINN architectures. The framework is validated against benchmark problems with known analytical solutions, demonstrating superior accuracy and robustness. Additionally, proposed model is applied on real-world financial data where analytical solutions are unavailable, showcasing its practical utility in derivative pricing.Our findings demonstrate that the proposed method offers a high-precision, scalable alternative to traditional solvers, while also advancing the integration of fractional calculus and deep learning. This work contributes to the development of interpretable and robust models in computational finance, highlighting the potential of physics-informed machine learning in addressing complex financial systems.
11:10 AM – 11:30 AM 115-B Short Communications

Lifting of Fischer Matrices Method

  • Abraham Prins (University of Fort Hare)
Bernd Fischer developed the Fischer matrices method based on Clifford theory, which is a technique used to construct the ordinary character tables of finite group extensions. It is well known that the ordinary irreducible characters of a factor group can be lifted to the full group. Let $\overline{G}=P{.}G$ be a finite extension of a $p$-group $P$ by a group $G$ and consider the factor group $\overline{F}=\frac{\overline{G}}{K}$, where $K\trianglelefteq \overline{G}$ is a characteristic subgroup of $P$. In this talk, we introduce the lifting of Fischer matrices method, which is a technique for constructing a Fischer matrix of $\overline{G}$, denoted $M(g)$, from the corresponding Fischer matrix $\widehat{M(g)}$ of $\overline{F}$. We will illustrate this technique to demonstrate how the Fischer matrices of the maximal subgroup $MS=2^{9+16}{{}^\cdot}Sp_8(2)$ of the simple Baby Monster group $\mathbb{B}$ can be derived from the Fischer matrices of an underlying factor group with structure $2^{1+16}{{}^\cdot}Sp_8(2)$ and how these matrices can then be used to construct the character table of $MS$.
11:10 AM – 11:30 AM 115-A Short Communications

Well-Posedness of Nonlinear Coupled Systems Modelling MEMS

  • Runan He (Instituto de Ciencias Matemáticas (ICMAT))
This talk introduces the study of some mathematical models for a Micro-Electro-Mechanical System (MEMS) capacitor, consisting of a fixed plate and a flexible plate separated by a fluid. It investigates the wellposedness of solutions to the resulting quasilinear coupled systems, as well as the finite-time blow-up (quenching) of solutions. The models considered include a parabolic-dispersive system modelling the fluid flow under an elastic plate, a parabolic-hyperbolic system for a thin membrane, as well as an elliptic-dispersive system for quasistatic fluid flow under an elastic plate. Short-time existence, uniqueness and smoothness are obtained by combining wellposedness results for a single equation with an abstract semigroup approach for the system. Quenching is shown to occur, if the solution ceases to exist after a finite time.
11:10 AM – 11:30 AM 115-C Short Communications

Zero-Dilation Indices and Numerical Ranges

  • Paul Reine Kennett Dela Rosa (University of the Philippines Diliman)
The zero-dilation index $d(A) $ of a matrix $A$ is the largest integer $k$ for which $\begin{bmatrix}0_k& *\\ * & *\end{bmatrix}$ is unitarily similar to $A$. In this study, the zero-dilation indices of certain block matrices are considered, namely, the block matrix analogues of companion matrices and upper triangular KMS matrices, respectively shown as \[\mathcal{C}=\begin{bmatrix} 0& \bigoplus_{j=1}^{m-1}A_j \\ B_0& [B_j]_{j=1}^{m-1}\end{bmatrix}\ \textup{and}\ \mathcal{K}=\begin{bmatrix}0& A& A^2&\cdots& A^{m-1}\\ 0 & 0& A& \ddots& \vdots\\ 0& 0 &0 &\ddots& A^2\\ \vdots& \vdots &\vdots & \ddots& A\\ 0& 0 & 0& \cdots &0\end{bmatrix}\]where $\mathcal{C}$ and $\mathcal{K}$ are $mn$-by-$mn$ and $A_j,B_j,A$ are $n$-by-$n$. Provided $\bigoplus_{j=1}^{m-1}A_j$ is nonsingular, it is proved that $d(\mathcal{C})$ satisfies the following: if $m\geq 3$ is odd (respectively, $m\geq 2$ is even), then $\frac{(m-1)n}{2}\leq d(\mathcal{C})\leq \frac{(m+1)n}{2}$ (respectively, $ d(\mathcal{C})= \frac{mn}{2}$). In the odd $m$ case, examples are given showing that it is possible to get as zero-dilation index each integer value between $\frac{(m-1)n}{2} $ and $\frac{(m+1)n}{2}$. On the other hand, $d(\mathcal{K})$ is proved to be equal to the number of nonnegative eigenvalues of $(\mathcal{K}+\mathcal{K}^*)/2$. Alternative characterizations of $d(\mathcal{K})$ are given. The circularity of the numerical range of $\mathcal{K} $ is also considered.
11:30 AM – 11:50 AM 115-A Short Communications

Convergence of the Energy and Correctors for Some Elliptic Problems in a Two-Component Domain with Weak Data

  • Rheadel Fulgencio (University of the Philippines - Diliman)
In this talk, we discuss the convergence of the energy and the corrector results of the homogenization results obtained by Donato et al. for the following class of elliptic problems: $$\begin{cases}-\operatorname{div} (A^{\varepsilon}(x,u_1^{\varepsilon})\nabla u_1^{\varepsilon}) = f \quad &\mbox{in }\Omega_1^\varepsilon,\\-\operatorname{div} (A^{\varepsilon}(x,u_2^{\varepsilon})\nabla u_2^{\varepsilon}) = f \quad &\mbox{in }\Omega_2^\varepsilon,\\u^{\varepsilon}_1=0\quad &\mbox{on }\partial\Omega,\\(A^{\varepsilon}(x,u^{\varepsilon}_1)\nabla u^{\varepsilon}_1)\nu_1^\varepsilon = (A^{\varepsilon}(x,u^{\varepsilon}_2)\nabla u^{\varepsilon}_2)\nu_1^\varepsilon \quad&\mbox{on }\Gamma^{\varepsilon},\\(A^{\varepsilon}(x,u^{\varepsilon}_1)\nabla u^{\varepsilon}_1)\nu_1^\varepsilon = -\varepsilon^{-1}h^\varepsilon(x)(u^{\varepsilon}_1-u^{\varepsilon}_2) \quad&\mbox{on }\Gamma^{\varepsilon},\end{cases} $$ where $\Omega$ is a two-component domain with components $\Omega_1^\varepsilon$ (a connected domain) and $\Omega_2^\varepsilon$ (a disconnected union of small $\varepsilon$-periodic sets), and $\Gamma^\varepsilon = \partial\Omega_2^\varepsilon$ serves as the interface between the components. We prescribe $L^1$ data and coefficient periodic matrix fields $A(y,t)$ only bounded for bounded $t$, so that we deal with renormalized solutions, where only their truncated solutions are in $H^1$.We present here some important results obtained such as the convergence of the unfolded truncated energies to the truncated energy of the homogenized problem and the strong convergence of the truncated gradients (which was only proven as weak in a previous work). These convergences allow us to obtain some corrector results in the linear case, where $A$ does not depend on $t$.
11:30 AM – 11:50 AM 116-A Short Communications

MHD Flow and Heat Transfer Enhancement in Micropolar Casson Hybrid Nanofluid: Nanofluid Versus Hybrid Nanofluid

  • ABID HUSSANAN (University of Education, Lahore, Multan Campus, Pakistan)
Hybrid nanofluids are considered advanced nanofluids due to their enhanced thermal properties and significant benefits that contribute to increasing the heat transfer rate. Therefore, scientists and researchers are incorporating various solid particles into base fluids to enhance the material's thermal conductivity. This study presents the heat transfer and magnetohydrodynamic (MHD) flow characteristics of a micropolar Casson hybrid nanofluid composed of Sodium Alginate (SA) with the Prandtl number Pr  =  6.45, as the base fluid and copper (Cu) and aluminum oxide (Al₂O₃) nanoparticles. The research aims to enhance heat transfer performance and fluid stability through the interactive effects of hybrid nanoparticles. A mathematical model is developed to investigate the effects of magnetic fields on rheological parameters, with governing equations formulated for a steady flow over a stretching surface. The converted ordinary differential equations are solved numerically using the Runge-Kutta-Fehlberg (RKF) method to determine the impacts of magnetic, Casson, and micro-rotation parameters on velocity and temperature profiles. Comparative results reveal that hybrid nanofluids demonstrate more heat dissipation and enhanced thermal management properties over traditional nanofluids.
11:30 AM – 11:50 AM 115-C Short Communications

On Generalized p.q.-Baer $*$-rings

  • Anil Khairnar (Abasaheb Garware College)
We introduced the class of weakly generalized p.q.-Baer $*$-rings. It is proved that under some assumptions every weakly generalized p.q.-Baer $*$-ring can be embedded in generalized p.q.-Baer $*$-ring. We proved that a generalized p.q.-Baer $*$-rings has partial comparability. If a generalized p.q.-Baer $*$-ring satisfies the parallelogram law then it is proved that every pair of projections has an orthogonal decomposition. A separation theorem for generalized p.q.-Baer $*$-rings is obtained. As an application of spectral theory, it is proved that generalized p.q.-Baer $*$-rings have a sheaf representation with injective sections.
11:30 AM – 12:30 PM Terrace Ballroom Plenary Lecture

Optimization in Theory and Practice

  • Stephen Wright (University of Wisconsin-Madison)
Algorithms for continuous optimization problems have a rich history of design and innovation over the past several decades, in which mathematical analysis of their convergence and complexity properties plays a central role. Besides their theoretical properties, optimization algorithms are interesting also for their practical usefulness as computational tools for solving real-world problems. There are often gaps between the practical performance of an algorithm and what can be proved about it. These two facets of the field - the theoretical and the practical - interact in fascinating ways, each driving innovation in the other. This work focuses on the development of algorithms in two areas - linear programming and unconstrained minimization of smooth functions - outlining major algorithm classes in each area along with their theoretical properties and practical performance, and highlighting how advances in theory and practice have influenced each other in these areas. In discussing theory, we focus mainly on non-asymptotic complexity, which are upper bounds on the amount of computation required by a given algorithm to find an approximate solution of problems in a given class.
11:30 AM – 11:50 AM 115-B Short Communications

Primary Decomposition in S-Noetherian Modules

  • SHIV DATT KUMAR (Motilal Nehru National Institute of Technology Allahabad, Prayagraj, India)
Let $R$ be a commutative ring with identity, $S\subseteq R$ be a multiplicative set, and $M$ be an $R$-module. We say that a submodule $N$ of $M$ with $(N:_RM)\cap S=\emptyset$ has an $S$-primary decomposition if it can be written as a finite intersection of $S$-primary submodules of $M$. Let $Q$ be a submodule of an $R$-module $M$ with ${(Q:_RM)}\cap S=\emptyset$, where $(Q:_RM)=\{r\in R\hspace{0.1cm}|\hspace{0.1cm} rM\subseteq Q\}$. Then $Q$ is said to be an $S$-primary submodule if there exists $s\in S$ such that for all $a\in R$ and $m\in M$ if $am\in Q$, then either $sa\in\sqrt{(Q:_RM)}$ or $sm\in Q$. Following is an example of an $S$-Noetherian module in which primary decomposition does not exist.\begin{example} Let $R=\mathbb{F}[x_1,x_2,\ldots, x_{n}, \ldots]$ be a polynomial ring in infinitely many indeterminates over a field $\mathbb{F}$ and $M=(x_1,x_2,\ldots, x_{n}, \ldots)$. Then $M$ is not Noetherian $R$-module and hence a non-Laskerian module. Consider a multiplicative set $S=R\setminus\{0\}$. Let $N$ be a non-zero submodule of $M$ and $0 \neq f\in N$. Then $f\in S$. Take $s=f\in S$. This implies that $sN\subseteq sM\subseteq sR\subseteq N.$ Put $K=sR$. Then $K$ is finitely generated submodule of $N$ such that $sN\subseteq K\subseteq N$. Hence $N$ is $S$-finite, and $M$ is an $S$-Noetherian module but not a Laskerian module.\end{example}\begin{theorem}(\textbf{$S$-Primary Decomposition})Let $M$ be an $S$-Noetherian $R$-module. Then every proper submodule $N$ with $(N:_RM)\cap S=\emptyset$ can be written as a finite intersection of $S$-primary submodules.\end{theorem}\begin{theorem} Let $R$ be an $S$-Noetherian ring and $M$ a finitely generated $R$-module. Let $(0)=N_1\cap N_2\cap\cdots \cap N_r$ be reduced $S$-primary decomposition of $0$ in $M$, $N_{i}$ being $S$-$P_{i}$-primary $(1\leq i\leq r)$, where $P_{i}$ is $S$-prime. If $S$ contains no zero-divisors of $M/N_{i}$ for all $i=1,2,\ldots,r$, then $Ass(M)=\{P_1,P_2,\ldots, P_r\}$. \end{theorem}\begin{theorem} Let $N$ be a submodule of $R$-module $M$ such that $N=\bigcap\limits_{i=1}^{n}N_{i}$ is a minimal $S$-primary decomposition, where $N_{i}$ is $S$-$P_{i}$-primary submodule of $M$. Then for each $x\in R$, $P_{i}$ is precisely the $S$-prime ideal satisfying $sP_{i}\subseteq s'\sqrt{((N:_Mx):_RM)}\subseteq P_{i}$ for some $s,s'\in S$. Also these $P_i$ are independent of decomposition of $N$.\end{theorem}
11:50 AM – 12:10 PM 115-A Short Communications

Analytical Solutions and Conservation Laws for the First Extended Modified (3+1)-dimensional Integrable Vakhnenko-Parkes Equation

  • Chaudry Khalique (North-West University)
In this talk we present analytical examination of the first extended modified Vakhnenko-Parkes equation, namely $u u_{txx} - u_{x} u_{tx} + u^3 u_{t}+ a u_{x}+ b u_{y} + c u_{z}=0$, where $a$, $b$, and $c$ are real valued nonzero constant parameters, using the Lie group analysis approach along with the extended Jacobi elliptic function expansion technique. We determine abundant structures of analytical solutions of this equation. This approach adopts the use of three different auxiliary nonlinear ordinary differential equations to generate the solutions. Thus, we find diverse cnoidal, snoidal, dnoidal, as well as complex snoidal wave solutions. Moreover, we explore the wave dynamics of these periodic solutions in three dimensions and two dimensions using computer software. Finally, we generate conserved vectors associated to the point symmetries of the equation using Ibragimov's theorem via the formal Lagrangian of the model.
11:50 AM – 12:10 PM 115-C Short Communications

Key-Exchange Protocols Based on Split-Octonions and Zero Divisors

  • EL HAOUI YOUSSEF (Ecole Normale Supérieure, Moulay Ismail university of Meknes)
Split-octonions form an eight-dimensional, non-associative, non-commutative algebra equipped with a quadratic pseudo-norm and containing zero divisors. Leveraging this structure, we propose a key-exchange protocol where parties generate random non-invertible identifiers, and the public communication identifier is constructed via quaternionic decomposition. Subkeys are exchanged and combined into a shared session key, with correctness guaranteed by the right Moufang identity. Efficient algorithms are developed for split-octonion multiplication and coefficient encoding/decoding, and numerical examples are provided to demonstrate the protocol’s effectiveness. This work highlights a novel use of pseudo-norms and non-associative algebras in cryptography, suggesting broader applications of higher-dimensional composition algebras in secure communications.
11:50 AM – 12:10 PM 115-B Short Communications

Orthogonal Jordan Derivations on Γ-Semihyperrings

  • Kishor Pawar (Kavayitri Bahinabai Chaudhari North Maharashtra University, Jalgaon)
We introduce the concept of orthogonal derivations on $\Gamma$-semihyperrings and explore some fundamental properties of orthogonal Jordan derivations. It is shown that a non-zero derivation is not necessarily orthogonal to itself and we establish the specific conditions under which such a derivation becomes orthogonal to itself. Furthermore, we prove that the sum of two orthogonal derivations remains orthogonal to each of its summands. A necessary and sufficient condition for two derivations to be orthogonal is also derived.
12:10 PM – 12:30 PM 115-B Short Communications

Generator Sets for the Magma Monoid

  • Isaac Owusu-Mensah (University of Skills Training and Entrepreneurial Development)
In this talk, we will explore the algebraic structures of the magma monoid $(\mathcal{M}(S), \triangleleft)$, where $\mathcal{M}(S)$ comprises all binary operations on $S$. We investigate the order and generator set of elements characterizing idempotents, almost constant operations, and units - facilitating our analysis. A procedure for finding inverses of units is presented, along with key results on almost constant operations. Focusing on $|S|= 2$ and $|S|= 3$, we classify the elements into various categories, determine their orders and identify generating sets for the magma monoid. These findings inform a concise methodology for identifying the generator sets of an arbitrary element $\ast \in \mathcal{M}(S)$.
12:10 PM – 12:30 PM 115-C Short Communications

Injectivity of Topological Modules

  • Yunita Septriana Anwar (Universitas Muhammadiyah Mataram)
Let $R$ be a topological ring and $M$ a topological $R$-module. A module $U$ is called a topological $M$-injective module if for every continuous monomorphism $f \colon K \to M$, where $K$ is an open submodule of $M$, and for every continuous homomorphism $g \colon K \to U$, there exists a continuous homomorphism $h \colon M \to U$ such that $hf = g$. A topological $M$-injective module is a topological injective module relative to all topological $R$-modules in the category $Top_{\sigma[M]}$. The direct product of topological $M$-injective modules in the categories $Top_{R\text{-}MOD}$ and $Top_{\sigma[M]}$ is also a topological $M$-injective module. An infinite direct sum of topological $M$-injective modules is again topological $M$-injective provided that the direct sum is an open submodule of the direct product of the topological $M$-injective modules.The topological $M$-injective hull of a topological module $N$ is a minimal topological $M$-injective module containing $N$. Injectivity of infinite direct sums of injective modules does not necessarily hold in general, and the existence of injective hulls is not guaranteed in arbitrary categories. If $(N,\tau) \in Top_{\sigma[M]}$, then $N$ admits a topological injective hull in $Top_{\sigma[M]}$, namely the topological trace $Tr^{*}(M,E_{\tau}(N))$, where $E_{\tau}(N)$ is the topological injective hull of $N$ in $Top_{R\text{-}MOD}$. Furthermore, if $(N,\tau) \in Top_{\sigma[M]}$, the injective hulls of $N$ in the categories $R\text{-}MOD$, $\sigma[M]$, $Top_{R\text{-}MOD}$, and $Top_{\sigma[M]}$ are respectively denoted by $E(N)$, $\widehat{N}$, $E_{\tau}(N)$, and $\widetilde{N}$. The relationships among these injective hulls are given by\[N \subseteq Tr^{*}(M,E_{\tau}(N)) \subseteq E_{\tau}(N) \subseteq E(N)\]and\[N \subseteq Tr^{*}(M,E_{\tau}(N)) \subseteq Tr(M,E(N)) \subseteq E(N).\]Compactness in topological spaces is closely related to finiteness properties in topology. For a topological module in $Top_{\sigma[M]}$, a compact topological $M$-injective module containing it does not always exist. In particular, for non-precompact topological modules and locally compact topological modules, there is no compact topological $M$-injective module containing them, whereas a compact topological module can be embedded into a compact topological $M$-injective module.
12:10 PM – 12:30 PM 115-A Short Communications

Mixed Initial-Boundary-Transmission Problems for Complex Multi-Layered Structures

  • David Natroshvili (Georgian Technical University)
We investigate dynamic mixed initial-boundary-transmission problems of the generalized thermo-electro-magneto elasticity theory for complex elastic multi-component structures containing interior and interfacial cracks. Theoretical study of such problems attracts great attention due to the widespread use of modern sensing and actuating devices based on the ability to transform mechanical, electric, magnetic, and thermal energies from one form to another. Therefore, the mathematical models taking into consideration coupling effects between thermo-mechanical and electromagnetic fields in elastic composites became very popular during the last decades In each component of the composed body, we consider Green-Lindsay’s generalized model with different material constants. A remarkable feature of this model is that the speed of heat propagation is finite in contrast to infinite speed of heat transfer which occurs in the classical theory.We apply Laplace transform to reduce the dynamic mixed transmission problems to the corresponding elliptic problems for the so-called pseudo-oscillation differential equations depending on a complex parameter. We apply the potential method and the theory of pseudodifferential equations and analyse smoothness properties and asymptomatic behaviour of solutions to the elliptic pseudo-oscillation problems near the edges of cracks and near the curves where different types of boundary conditions collide. We describe algebraic algorithms for finding explicitly the stress singularity exponents and analyse their dependence on material parameters. We estimate the norms of solutions to the elliptic pseudo-oscillation problems in appropriate function spaces with respect to the complex parameter and by the inverse Laplace transform we reconstruct the solutions of the original mixed dynamic problems. Using the corresponding asymptotic behaviour near the exceptional curves (crack edges and collision curves) we obtain the optimal regularity results of solutions and describe dynamical stress singularities. We analyse in detail arising of oscillating stress singularities depending on the material parameters. This is a joint work with O.Chkadua and T.Buchukuri.Acknowledgments. This work was supported by Shota Rustaveli National Science Foundation of Georgia (SRNSF) (Grant number FR-23-267).
12:30 PM – 12:50 PM 115-C Short Communications

A Combinatorial Technique for Rational Representations and Rational Group Algebras of Metacyclic $p$-groups

  • Ram Karan Choudhary (Indian Institute of Science Education and Research, Pune)
In this talk, I will present a combinatorial formula for computing the Wedderburn decomposition of the rational group algebra $\mathbb{Q}G$, where $G$ is a metacyclic $p$-group for any prime $p$. I will also introduce a formula to count the irreducible rational representations of $G$ with distinct degrees. Furthermore, I will outline a method for explicitly constructing all inequivalent irreducible rational matrix representations of $G$.
12:30 PM – 1:30 PM Breaks

Lunch on Own

12:30 PM – 1:30 PM Benjamin Franklin Stage Films @ ICM

Olga Ladyzhenskaya & Math Circles Around the World (Double Feature)

Film Directed by Ekaterina Eremenko

The film tells the story of Olga Aleksandrovna Ladyzhenskaya, a world-famous mathematician, a very beautiful, bright, intelligent and charismatic person. Many of Ladyzhenskaya’s ideas influenced the development of modern mathematical physics.

Source: Discretization in Geometry and Dynamics

 

 

12:30 PM – 12:50 PM 115-A Short Communications

Phase Transitions in Quantum Walks

  • Mikhail Skopenkov (King Abdullah University of Science and Technology)
Quantum walks, introduced by Richard Feynman, are archetypical for studying quantum algorithms. A one-dimensional quantum walk exhibits a phase transition: the wave function oscillates inside some region but exponentially decreases outside. The large-time asymptotic behavior at the transition point is described by the Airy function, as proved by Sunada and Tate in 2012. For the first time, we prove a uniform asymptotic formula in the whole domain and discover another type of phase transition, which also appears in many other models. We prove a general theorem producing uniform asymptotic formulae of this kind from certain conformal mappings.This is joint work with M. Drmota, F. Kuyanov, and A. Ustinov.
12:30 PM – 12:50 PM 115-B Short Communications

Sharp Quantitative Stability Estimates in Caffarelli-Kohn-Nirenberg Type Inequalities

  • Anh Do (University of Connecticut)
Quantitative stability for functional and geometric inequalities plays a significant role in the calculus of variations and evolution partial differential equations. Once the set of all optimizers is fully characterized, natural questions on stability results arise about estimating the distance to the manifold of optimizers via the deficit, which is the difference between the two sides of the inequality. Such stability results have wide-ranging applications, including the justification of Taylor expansions and spectral estimates in mathematical physics, as well as a posterior error analysis in numerical methods.Since the foundational work of Bianchi and Egnell, there has been growing interest in developing quantitative stability results. In this talk, we present recent advances in the study of the stability for Caffarelli–Kohn–Nirenberg (CKN) inequalities, which encompass and generalize several classical inequalities, including Sobolev and Gagliardo–Nirenberg inequalities. We first provide a complete classification of $L^2$-stability results for all parameter regimes, extending and completing earlier work by Cazacu, Flynn, Lam, and Lu. In addition, using an alternative method that avoids spherical harmonics decomposition, we establish new $L^p$-stability results. Motivated by recent work of Dolbeault, Esteban, Figalli, Frank, and Loss, the sharpness of stability constants has emerged as a central topic. Addressing an open question posed by Maz'ya, we obtain sharp stability results for the Heisenberg Uncertainty Principle (HUP) in the setting of second-order and curl-free vector fields. To further generalize these findings, we derive new $L^2$-stability results for HUP by introducing several weighted Poincaré inequalities with Gaussian measures on hyperbolic spaces, where classical scaling arguments are no longer applicable. This talk is based on joint work with Guozhen Lu, Nguyen Lam, Nguyen Van Hoang, Debdip Ganguly, Joshua Flynn, and Lingxiao Zhang.
12:50 PM – 1:10 PM 115-A Short Communications

Isometries and Metric Properties of Quantum Wasserstein Distances

  • Dániel Virosztek (HUN-REN Alfréd Rényi Institute of Mathematics)
Although the theory of classical optimal transport has been playing an important role in mathematical physics (especially in fluid dynamics) and probability since the late 80s, concepts of optimal transportation in quantum mechanics have emerged only very recently. We briefly review the most relevant approaches and discuss a non-quadratic generalization of the quantum mechanical optimal transport problem introduced by De Palma and Trevisan, where quantum channels realize the transport. Relying on this general machinery, we introduce p-Wasserstein distances and divergences and study their fundamental geometric properties. Finally, we demonstrate that the quadratic quantum Wasserstein divergences are genuine metrics, and summarize our recent results on the isometries of the qubit state space with respect to Wasserstein distances induced by distinguished transport cost operators.
12:50 PM – 1:10 PM 115-C Short Communications

K\"oethe Conjecture Revisited: An Introduction to Quasi Reduced Rings

  • Puguh Wahyu Prasetyo (Universitas Ahmad Dahlan)
The Koethe conjecture was proposed by Gottfried Koethe in 1930. It states: In any ring, the sum of a nilpotent subring and a nil subring is nil. It holds true for several significant classes of rings, including all right Noetherian rings and quasi $2-$primal rings. In this paper, we work on $2-$primal rings, weakly $2-$primal rings, and quasi $2-$primal rings as key elements in our investigation. We introduce a quasi reduced ring as a generalization of a reduced ring and prove that quasi reduced rings also satisfy the Koethe conjecture. The class of all quasi reduced rings is denoted by $\mathcal{Q}_\mathcal{R}$. We technically show that the class $\mathcal{Q}_\mathcal{R}$ of all quasi reduced rings forms a weakly special class of rings and it is precisely the semisimple class $\mathcal{S}\mathcal{K}$ of the Koethe nilradical $\mathcal{K}$ which implies that the upper radical $\mathcal{U}(\mathcal{Q}_\mathcal{R})$ is precisely the Koethe nilradical $\mathcal{K}$. We also provide a taxonomy related to $2-$primal rings, weakly $2-$primal rings, quasi $2-$primal rings, and quasi reduced rings. Finally, we give necessary and sufficient conditions for the Koethe conjecture to have a positive answer in quasi reduced ring perspective.
12:50 PM – 1:10 PM 115-B Short Communications

Nonuniqueness of Solutions to the Two-Dimensional Euler Equations with Integrable Vorticity

  • Anuj Kumar (University of California Davis)
Yudovich established the well-posedness of the two-dimensional incompressible Euler equations for solutions with bounded vorticity. DiPerna and Majda proved the existence of weak solutions with vorticity in $L^p ( p > 1)$. A celebrated open question is whether the uniqueness result can be generalized to solutions with $L^p$ vorticity. In this talk, we resolve this question in negative for some $p > 1$. To prove nonuniqueness, we devise a new convex integration scheme that employs non-periodic, spatially-anisotropic perturbations, an idea that was inspired by our recent work on the transport equation. To construct the perturbation, we introduce a new family of building blocks based on the Lamb-Chaplygin dipole. This is a joint work with Elia Bru\`e and Maria Colombo.
1:10 PM – 1:30 PM 115-A Short Communications

Geometric Reconstruction of Dark Energy in Modified Symmetric Teleparallel Gravity: A Mathematical Framework Beyond Riemannian Geometry

  • Sanjeeda Sultana (Amity University, Kolkata)
In this work, we present a novel reconstruction of a dark energy model within the framework of modified symmetric teleparallel gravity, formulated beyond the standard Riemannian paradigm. By integrating entropy-based dark energy formulations with a geometrically generalized theory of gravity that allows for non-metricity $Q$, we propose a mathematically consistent framework capable of capturing the dynamics of late-time cosmic acceleration. The resulting model exhibits a rich parametric structure, with the equation of state (EoS) parameter and deceleration parameter showing pronounced sensitivity to both the initial conditions and the underlying parameter space. To ensure observational viability, we perform a comprehensive Markov Chain Monte Carlo (MCMC) analysis using combined cosmological datasets, yielding best-fit parameter values that are in excellent agreement with current observational constraints. The reconstructed cosmological evolution is further validated through an independent computation of the cosmic age, reinforcing the internal consistency of the model. Geometrical diagnostics, including the evolution of the statefinder pairs $(r,s)$ and $(r,q)$, reveal that the model trajectories transit through the $\Lambda$CDM fixed point, affirming its concordance with standard cosmological behavior in the appropriate limits. In addition, a detailed examination of the classical energy conditions confirms the model’s physical admissibility across a wide range of parameters. This study highlights the potential of non-metric geometric formulations as a fertile ground for advancing theoretical models of dark energy and provides a mathematically rigorous pathway for embedding cosmological phenomena within generalized differential geometric structures.
1:10 PM – 1:30 PM 115-C Short Communications

MHD Trihybrid Nanofluid Flow with Hall Current and Electric Field Effects: Numerical and Neural Network Analysis

  • RAJ NANDKEOLYAR (National Institute of Technology Jamshedpur)
This study investigates the importance of Magnetohydrodynamic (MHD) trihybrid nanofluid flow across a stretching surface. The combination of silicone oil-based silver ($Ag$), magnesium oxide ($MgO$), and Titanium dioxide ($TiO_2$) nanofluids has attracted attention for its potential to improve fluid performance. The research accounts for the combined influence of Hall current and electric field on the flow, while also exploring the effects of nonlinear thermal radiation and Joule heating. A mathematical model is developed to address the core problem, incorporating nonlinear partial differential equations (PDEs) with suitable boundary conditions. These PDEs are transformed into ordinary differential equations (ODEs) using similarity transformations and solved numerically via the SQLM method. The impact of each parameter is evaluated and presented through graphical illustrations. The study proposes a novel approach for advanced numerical computation by employing a multi-layer perceptron (MLP) feed-forward back-propagation Artificial Neural Network (ANN) integrated with the Levenberg-Marquardt algorithm (LMB). Various parameters were systematically varied using SQLM to create a dataset optimized for refining the ANN-LMB model across different scenarios. Data collection included testing, validating, and training the ANN model. The ANN-LMB methodology was validated through regression analysis, mean squared error (MSE) assessment, and histogram evaluations.
1:10 PM – 1:30 PM 115-B Short Communications

Riemann Problem and Delta Shock Interactions in Generalized Chaplygin Gas with Source Term

  • MINHAJUL MINHAJUL (BITS Pilani, K K Birla Goa Campus)
In this talk, we consider the Riemann problem and wave interactions for the one-dimensional generalized Chaplygin gas equations with a nonlinear time-dependent source term. We discuss the construction of the Riemann solution for this nonhomogeneous hyperbolic system and show that the solution contains a singularity under certain conditions in the initial data; that is, a $\delta$-shock wave arises in the solution. Consequently, we derive the speed, position, and strength of the $\delta$-shock using the $\delta$-entropy condition. Finally, we discuss the wave interactions involving the $\delta$-shock wave to establish the global solution by taking three piecewise constant perturbed initial data.
1:30 PM – 1:50 PM 115-B Short Communications

Diophantine Approach to Understanding Surface Area and Volume Ratios in Prisms

  • Jerico Bacani (University of the Philippines Baguio)
This study explores the interplay between number theory and geometry using the Diophantine equation $\frac{1}{x} + \frac{1}{y} + \frac{1}{z}=\frac{1}{n}$, where $x, y$ and $z$ are positive integers. We derive and analyze solutions for $n = 4, 5, 6$ and use Python to determine solutions for higher values of $n.$ The study then connects these number-theoretic results to geometry by using the solutions as dimensions of prisms --- rectangular, right triangular, and regular $p$-gonal prisms. We analyze how the surface area to volume (SA/V) ratios vary with $n$ and prism type. For rectangular prisms, it is trivial that the SA/V ratio simplifies to $\frac{2}{n}$, while for other prism types, the expressions involve more complicated dependencies on $n$, the base shape, and apothem length. Explicit formulas for SA/V for such geometries shall be presented.
1:30 PM – 1:50 PM 115-A Short Communications

Expanded Regimes of Area Law for Lattice Yang-Mills Theories

  • Ron Nissim (Massachusetts Institute of Technology)
We extend the parameter regimes under which the area law is proven for pure $\mathrm{U}(N)$ lattice Yang-Mills theories, particularly in the large-$N$ limit, in joint work with Sky Cao and Scott Sheffield. In this talk, I will begin by reviewing the $\mathrm{U}(N)$ lattice Yang-Mills model and the celebrated area law conjecture, which is believed to explain the physical phenomenon of quark confinement. I will then compare our theorem with classical previously known results, which our work directly improves upon in dimension four and higher for large $N$. Following that, I will introduce the main tool in our analysis: the master loop equation. I will provide intuition for our result by interpreting the master loop equation as a process of surface exploration. Finally, I will present the technical framework in which the master loop equation is studied as a fixed-point problem, and the challenge to this approach posed by the "merger" term of the master loop equation.
1:30 PM – 1:50 PM 115-C Short Communications

Modulation of the Vector Potential of the Core of an Elliptical Vortex of the Second Rank with the Distribution of Right- and Left-Handed Matter Flows

  • Algimantas Milyus (IRG "LITAVEM-3")
This paper investigates the dynamics and interaction mechanisms of swirling flows that carry right- and left-hand rotation, maintaining the mass transfer circulation inside an elliptical closed vortex structure. The study focuses on the modulation of the vector potential core in a second-rank elliptical vortex and its effect on the flow polarity distribution and the overall vorticity balance.A theoretical framework is proposed to describe how the modulation of the vortex kern affects the spatial separation and simultaneous propagation of right- and left-handed vortex flows. It is shown that these flows maintain independent coherence while simultaneously contributing to a continuous circulation field inside the vortex. The resulting configuration ensures the topological integrity of the overall vorticity field and supports stable coexistence of bipolar mass transport.A new concept is introduced: protection of autowaves in the vortex dynamics of the elliptical core. These self-sustaining wave structures exhibit morphological features that stabilize the trajectory of matter flows through geometric alignment and mutual "non-interference". The structural morphology of these autowaves ensures continuous, uninterrupted movement of two completely independent matter flows, which suggests a form of internal flow isolation supported by the geometry of the vortex kern.This analysis provides new insights into the role of global vortex vector potential modulation in maintaining the integrity of complex vortex systems in three dimensions. The proposed model may facilitate advanced interpretations of dual helicity, inverse lemniscatibility of the vortex flow in the discontinuity region, and chirality-driven transport phenomena in both natural and artificial vortex dynamics.
3:00 PM – 3:45 PM 122-AB Section Lecture

Elementary Subgroups in Isotropic Reductive Groups

  • Anastasia Stavrova (St. Petersburg Department of Steklov Mathematical Institute)
Let G be a reductive group (scheme) over a commutative ring R in the sense of SGA3 of M. Demazure and A. Grothendieck. In 2008 V. Petrov and the author defined the generalized elementary subgroup E_P(R) of the group of R-points G(R) as the subgroup generated by the R-points of the unipotent radicals of P and of an opposite parabolic subgroup P^-. This definition generalizes the well-known definition of an elementary subgroup of a Chevalley group (or, a split reductive group), as well as several other definitions of an elementary subgroup of isotropic classical groups over rings and simple algebraic groups over fields. We survey some basic properties of the generalized elementary subgroups E_P(R), and of the corresponding quotients G(R)/E_P(R) known as the non-stable K_1-functors, or the Whitehead groups, associated to G.
3:00 PM – 3:45 PM 121-AB

Higher Algebra and Stable Homotopy Groups

  • Tomer Schlank (University of Chicago)

A fundamental motivating problem in homotopy theory is to understand the higher
homotopy groups of spheres, \(\pi_n(S^k)\). Freudenthal's suspension theorem
shows that, for large \(k\), these groups depend only on the difference
\(m=n-k\). The resulting stable homotopy groups of spheres, denoted
\(\pi^S_m\), are finite for \(m>0\), and the sequence of finite abelian groups
\(\pi^S_m\) displays deep and fascinating patterns.

The mathematical object that organizes these groups is a \emph{spectrum}. In
this talk, I will explain the viewpoint that spectra are the homotopy-theoretic
analogues of abelian groups. Just as abelian groups form a foundational pillar
of algebra and algebraic geometry, spectra serve as the basic objects of
``higher algebra,'' an \(\infty\)-categorical form of algebra. From this
perspective, spectra can be studied through a local-to-global approach, by
decomposing them into so-called \emph{monochromatic layers}.

I will survey how higher algebra places the patterns in the stable homotopy
groups of spheres into a broader algebraic framework. I will then describe
recent advances in the study of monochromatic layers, including the disproof of
the long-standing Telescope Conjecture, and explain how these ideas lead to new
results on the asymptotic behavior and in particular asymptotic bounds on the
sizes of the stable homotopy groups of spheres.


 

3:00 PM – 3:45 PM 118-C Section Lecture

Hilbert's Sixth Problem: Particles and Waves

  • Yu Deng (University of Chicago)

A major part of Hilbert’s sixth problem asks for the mathematical justification of the passage from atomistic interactions to the laws of motion of continuum. In the classical particle setting, this corresponds to the well known program of going from Newtonian particle dynamics to fluid equations, via Boltzmann’s kinetic theory. In the wave setting, one starts from nonlinear dispersive equations and aims at deriving the wave kinetic equation, i.e. wave analog of Boltzmann’s equation. In this talk I will present recent works, joint with Zaher Hani and Xiao Ma, that provide answer to both problems (in Boltzmann-Grad limit), starting from hard sphere dynamics for particles, and the cubic nonlinear Schrödinger (NLS) equation for waves. The two proofs follow the same framework (with distinctive technical features), namely the propagation of cumulant formulas, in the form of Feynman diagrammatic expansions.

3:00 PM – 3:45 PM 118-AB Section Lecture

Randomized Combinatorial Problems, in Sparse and Mean-Field Settings

  • Nike Sun (Massachusetts Institute of Technology)
We give a survey of some developments within the past decade or so in the study of random constraint satisfaction problems (CSPs), in both sparse and mean-field settings. This includes random SAT (and NAE-SAT) and the perceptron model. We will mention some results on the nature of the solution space, as well as on algorithms and hardness. This lecture is based on joint works with Jian Ding and Allan Sly; Erwin Bolthausen, Shuta Nakajima, and Changji Xu; and Brice Huang and Mark Sellke.
4:00 PM – 4:45 PM 118-C Special Section Lecture

Bridges to Translational Tilings: From Domino to p-adic Sudoku

  • Rachel Greenfeld (Northwestern University)

The study of the structure of translational tilings has captivated mathematicians, scientists, and the general public for centuries and continues to thrive at the crossroads of analysis, combinatorics, dynamics, logic, number theory, and geometry. This vibrant field seeks to uncover the delicate divide between rigid structures and unpredictable, "wild" behaviors that arise when sets fill space by translations without gaps or overlaps. I will provide an overview of this study and discuss recent developments, highlighting its interdisciplinary nature.

4:00 PM – 4:45 PM 120-AB Section Lecture

Hard Rods and Box Ball Systems

  • Prof Pablo A. Ferrari (University of Buenos Aires and CONICET)
We review recent results on two one-dimensional deterministic evolutions: hard rods and box-ball systems, both featuring conservation of mass and velocities.In the first system, quasi-particles, and in the second, solitons, travel ballistically until they collide with another particle or soliton. When two particles collide, both jump, with the nature of the jumps depending on the system.The dynamics of both models admit the same linearized representation: a configuration at time zero is mapped to a two-dimensional locally finite point set in the space-velocity plane.The first coordinate of each point corresponds to the position, and the second to the velocity, of the associated particle or soliton.The set obtained by translating the spatial coordinate of each point by its velocity is isomorphic to the linearization of the system’s configuration at time one.Spatially homogeneous Poisson processes with sufficiently fast decaying velocity densities are invariant for both linearizations.The evolution of the hard-rod system is related to discrete versions of the Lévy-Chentsov Brownian motion with several parameters.We describe several scaling limits in both the Euler and diffusive regimes.
4:00 PM – 4:45 PM 121-AB Section Lecture

Kleinian Viewpoints on Higher Rank Worldsle

  • Dick Canary (University of Michigan)
This talk is designed to attract people who work on real hyperbolic manifolds to consider thinking about discrete subgroups of higher rank Lie groups. To that end, we breezily discuss some applications of the ideas from the theory of Kleinian groups in the higher rank setting.
4:00 PM – 4:45 PM 122-AB Section Lecture

Local Volumes of Klt Singularities and K-Stability

  • Ziquan Zhuang (Johns Hopkins University)
I will survey a local K-stability theory for Kawamata log terminal singularities, and discuss some of its interactions with the (global) K-stability of Fano varieties and the Minimal Model Program.
4:00 PM – 5:00 PM Hall E - Expo Poster Presentations

Poster Exhibition

"Fröhlich-Spencer contours in Multidimensional Long-Range Ising Models" by Rodrigo Bissacot (11 - Mathematical Physics)

"Cohomological vertex algebras" by Colton Griffin (11 - Mathematical Physics)

"Topological Stability of Beltrami Fields as a Framework for Flavor Symmetry Alignment" by Charles Grimm (11 - Mathematical Physics)

"Regularisation by noise of quasilinear partial differential equations" by Antoine Marie Bogso (12 - Probability)

"Statistical Geometrization: A Unified Measure-Theoretic and Probabilistic Resolution to the Riemann Hypothesis" by Kemal Gursoy (12 - Probability)

"Uniqueness of Invariant Measures for Stochastic Damped Anisotropic Navier–Stokes Equations on the Full Plane" by Siyu Liang (12 - Probability)

"LDP FOR TENSOR FORMS" by Reihaneh Malekian (12 - Probability)

"The Resolvent Method in Complex Dynamics with applications to building a bridge between Schramm–Loewner Evolutions and Random Matrix Theory, and beyond" by Vlad Margarint (12 - Probability)

"Multi-component matching queues with abandonment and buffers : Fluid, diffusion limit and large deviations" by Souvik Ray (12 - Probability)

"Lower deviations for critical branching processes with immigration" by Sadillo Sharipov (12 - Probability)

"A Dynamical Approach to Nodal Lines of Critical Random Fields" by menglin wang (12 - Probability)

"Optimal Stopping Problems for Real Options Driven by Short-Noise Processes" by Ini Adinya (18 - Stochastic and Differential Modelling)

"Stochastic Analysis of Epidemic Dynamics Under a Two-Threshold Control Policy" by Hassane Bouzahir (18 - Stochastic and Differential Modelling)

"Mathematical Modeling and Sensitivity Analysis of SynNotch-CAR-T Cells Identify Engineering Targets for Dynamic Tunability" by Alexander Diefes (18 - Stochastic and Differential Modelling)

"A Bayesian Approach in Pricing Insurance under Stochastic Gompertz Model with Health Risk Factors" by Anjali Lomugdang (18 - Stochastic and Differential Modelling)

"On Large Deviations in Nonlinear Filtering Theory in the Besov-Orlicz Space" by Dina Miora (18 - Stochastic and Differential Modelling)

"Hybridization of Stochastic Hydrological Models and Machine Learning Methods for Improving Rainfall-Runoff Modeling" by Stephen Moore (18 - Stochastic and Differential Modelling)

"Equity Premium in a Semimartingale Market When Jump Amplitudes Follow an Arbitrary, Normal, Binomial and Gamma Distributions While Assuming Some Selected Utility Functions" by George Mukupa (18 - Stochastic and Differential Modelling)

"On the Concept of Digital Pathogens and Their Impact on 'Technopandemics'" by Farai Nyabadza (18 - Stochastic and Differential Modelling)

"Stochastic Epidemic Models with Partial Information on Undetected Infections in the Transmission of Zika Virus" by Lillian Oluoch (18 - Stochastic and Differential Modelling)

"A Study of Overcompensatory Prey Growth on Discrete-Time Predator-Prey Model with Continuous and Seasonal Breeding" by Narendra Pant (18 - Stochastic and Differential Modelling)

"Mathematical Modelling for CTCE-9908 (a CXCR4 inhibitor) on B16 F10 Melanoma Cell Proliferation" by Avulundiah Edwin Phiri (18 - Stochastic and Differential Modelling)

"Can we save the Tasmanian devil and restore ecosystem balance in Tasmania? " by Megan Powell (18 - Stochastic and Differential Modelling)

"Boundary-Value Problems for Dynamic and Integro-Dynamic Equations on Time Scales" by Roza Uteshova (18 - Stochastic and Differential Modelling)

"Educational Games for Teaching Threshold Concepts in Mathematics" by Vedrana Mikulić Crnković (19 - Mathematical Education and Popularization of Mathematics)

"Teacher Educators’ Learning and Development in Blended Learning Contexts" by Chanroath Monita (19 - Mathematical Education and Popularization of Mathematics)

"Mobius equivariant maps between fields" by Sunil Chebolu (3 - Number Theory)

"Symmetry and the Riemann Zeta Function" by Joseph Dillon (3 - Number Theory)

"A Variant of the Congruent Number Problem" by Jerome Dimabayao (3 - Number Theory)

"Trees and valuation sequences generated by polynomials and rational functions over Z_p" by Olena Kozhushkina (3 - Number Theory)

"Performance of Classical Factorization Algorithms for Structured Integers" by Isabella Li (3 - Number Theory)

"Number Theory in Pell's Equation" by Dr. Ruma Manandhar (3 - Number Theory)

"A Computational Comparison of Lang-Trotter and Hardy-Littlewood Constants for CM Elliptic Curves" by Anish Ray (3 - Number Theory)

"Distribution of Values of Gaussian Hypergeometric Functions " by Neelam Saikia (3 - Number Theory)

4:00 PM – 5:00 PM Hall E - Expo Poster Presentations

Poster Presentation by Author

"Fröhlich-Spencer contours in Multidimensional Long-Range Ising Models" by Rodrigo Bissacot (11 - Mathematical Physics)

"Cohomological vertex algebras" by Colton Griffin (11 - Mathematical Physics)

"Topological Stability of Beltrami Fields as a Framework for Flavor Symmetry Alignment" by Charles Grimm (11 - Mathematical Physics)

"Regularisation by noise of quasilinear partial differential equations" by Antoine Marie Bogso (12 - Probability)

"Statistical Geometrization: A Unified Measure-Theoretic and Probabilistic Resolution to the Riemann Hypothesis" by Kemal Gursoy (12 - Probability)

"Uniqueness of Invariant Measures for Stochastic Damped Anisotropic Navier–Stokes Equations on the Full Plane" by Siyu Liang (12 - Probability)

"LDP FOR TENSOR FORMS" by Reihaneh Malekian (12 - Probability)

"The Resolvent Method in Complex Dynamics with applications to building a bridge between Schramm–Loewner Evolutions and Random Matrix Theory, and beyond" by Vlad Margarint (12 - Probability)

"Multi-component matching queues with abandonment and buffers : Fluid, diffusion limit and large deviations" by Souvik Ray (12 - Probability)

"Lower deviations for critical branching processes with immigration" by Sadillo Sharipov (12 - Probability)

"A Dynamical Approach to Nodal Lines of Critical Random Fields" by menglin wang (12 - Probability)

"Optimal Stopping Problems for Real Options Driven by Short-Noise Processes" by Ini Adinya (18 - Stochastic and Differential Modelling)

"Stochastic Analysis of Epidemic Dynamics Under a Two-Threshold Control Policy" by Hassane Bouzahir (18 - Stochastic and Differential Modelling)

"Mathematical Modeling and Sensitivity Analysis of SynNotch-CAR-T Cells Identify Engineering Targets for Dynamic Tunability" by Alexander Diefes (18 - Stochastic and Differential Modelling)

"A Bayesian Approach in Pricing Insurance under Stochastic Gompertz Model with Health Risk Factors" by Anjali Lomugdang (18 - Stochastic and Differential Modelling)

"On Large Deviations in Nonlinear Filtering Theory in the Besov-Orlicz Space" by Dina Miora (18 - Stochastic and Differential Modelling)

"Hybridization of Stochastic Hydrological Models and Machine Learning Methods for Improving Rainfall-Runoff Modeling" by Stephen Moore (18 - Stochastic and Differential Modelling)

"Equity Premium in a Semimartingale Market When Jump Amplitudes Follow an Arbitrary, Normal, Binomial and Gamma Distributions While Assuming Some Selected Utility Functions" by George Mukupa (18 - Stochastic and Differential Modelling)

"On the Concept of Digital Pathogens and Their Impact on 'Technopandemics'" by Farai Nyabadza (18 - Stochastic and Differential Modelling)

"Stochastic Epidemic Models with Partial Information on Undetected Infections in the Transmission of Zika Virus" by Lillian Oluoch (18 - Stochastic and Differential Modelling)

"A Study of Overcompensatory Prey Growth on Discrete-Time Predator-Prey Model with Continuous and Seasonal Breeding" by Narendra Pant (18 - Stochastic and Differential Modelling)

"Mathematical Modelling for CTCE-9908 (a CXCR4 inhibitor) on B16 F10 Melanoma Cell Proliferation" by Avulundiah Edwin Phiri (18 - Stochastic and Differential Modelling)

"Can we save the Tasmanian devil and restore ecosystem balance in Tasmania? " by Megan Powell (18 - Stochastic and Differential Modelling)

"Boundary-Value Problems for Dynamic and Integro-Dynamic Equations on Time Scales" by Roza Uteshova (18 - Stochastic and Differential Modelling)

"Educational Games for Teaching Threshold Concepts in Mathematics" by Vedrana Mikulić Crnković (19 - Mathematical Education and Popularization of Mathematics)

"Teacher Educators’ Learning and Development in Blended Learning Contexts" by Chanroath Monita (19 - Mathematical Education and Popularization of Mathematics)

"Mobius equivariant maps between fields" by Sunil Chebolu (3 - Number Theory)

"Symmetry and the Riemann Zeta Function" by Joseph Dillon (3 - Number Theory)

"A Variant of the Congruent Number Problem" by Jerome Dimabayao (3 - Number Theory)

"Trees and valuation sequences generated by polynomials and rational functions over Z_p" by Olena Kozhushkina (3 - Number Theory)

"Performance of Classical Factorization Algorithms for Structured Integers" by Isabella Li (3 - Number Theory)

"Number Theory in Pell's Equation" by Dr. Ruma Manandhar (3 - Number Theory)

"A Computational Comparison of Lang-Trotter and Hardy-Littlewood Constants for CM Elliptic Curves" by Anish Ray (3 - Number Theory)

"Distribution of Values of Gaussian Hypergeometric Functions " by Neelam Saikia (3 - Number Theory)

5:00 PM – 5:45 PM 118-C Section Lecture

A Duality Inspired Journey in Convex Geometric Analysis

  • Shiri Artstein-Avidan (Tel Aviv University)
We explore the field of convex geometric analysis through the prism of duality theory. We discuss the theoretical basis of, and the motivation for, studying order reversing involutions, mainly on classes of convex sets and functions. We discuss the different dualities which can appear and which share some basic structure, and their uniqueness. We give special emphasis on three main non-traditional examples, pertaining to geometric convex functions, pseudo-cones, and ball bodies. We use the Blaschke-Santal\'o inequalty from convex geometry as a testing ground for these dualities.
5:00 PM – 5:45 PM 122-AB Section Lecture

Better Than Square Root Cancellation in Number Theory

  • Adam Harper (University of Warwick)
The idea that sums of oscillating terms should "typically" exhibit squareroot cancellation is common across mathematics, both in heuristics and rigorous results. In the last decade, it has been realised that certain important sums in multiplicative number theory, such as sums of Dirichlet characters, typically exhibit a bit more than squareroot cancellation. The source of this extra cancellation is a fascinating connection with the phenomenon of critical multiplicative chaos, from probability and mathematical physics. I will try to survey some of this work, focusing on the number theoretic aspects of the arguments. I will also discuss some possible applications, including non-vanishing problems, and short interval or arithmetic progression problems beyond the so-called squareroot barrier.
5:00 PM – 5:45 PM 120-AB Section Lecture

Critical Long-Range Percolation

  • Tom Hutchcroft (California Institute of Technology)
Statistical mechanical systems at and near their points of phase transition are expected to exhibit rich, fractal-like behaviour that is independent of the small-scale details of the system but depends strongly on the dimension in which the model is defined. Moreover, many models are conjectured to have an upper critical dimension with important quantitative and qualitative differences between critical behaviour at, above, and below the upper critical dimension. For models with long-range interactions, one expects additional transitions between effectively long-range and effectively short-range regimes, with further marginal effects on the boundary of these two regimes, leading to (at least) eight qualitatively distinct forms of critical behaviour in total for each given model. We will give a broad overview of these conjectures aimed at a general mathematical audience before surveying the significant recent progress that has been made towards understanding them in the context of long-range percolation.
5:00 PM – 5:45 PM 121-AB Section Lecture

Mean Curvature Flow Through Singularities

  • Robert Haslhofer (University of Toronto)
We first give a general introduction to the mean curvature flow, and then discuss fundamental results established over the last ten years that yield a precise theory for the flow through singularities in three dimensions. With the aim of developing a satisfying theory in higher dimensions, we then describe our recent classification of all noncollapsed singularities in dimension four. Finally, we provide a detailed discussion of open problems and conjectures.
6:00 PM – 6:45 PM 118-C Section Lecture

Asymptotic Properties of Banach Spaces

  • Thomas Schlumprecht (Texas A&M University, College Station)
An asymptotic property of a Banach space X is a property which is defined by {\em asymptotic games,} in which one player chooses cofinite-dimensional subspaces of X and the second player chooses a vector in the sphere of that cofinite-dimensional subspace. This is repeated a finite or infinite number of times. The outcome is then a finite or infinite sequence (x_n) in the sphere of X. An asymptotic property of X is then defined by theproperty that the first player has or does not have a strategy to force the outcome (x_n) to have a specific property, for example, to be isomorphic to the \ell_p-unit vector basis. We will apply this concept to solve several embeddings, universality problems, and problems concerning the coarse geometry of Banach spaces.
6:00 PM – 6:45 PM 122-AB Section Lecture

Quantitativity in The Mordell Conjecture

  • Xinyi Yuan (BICMR, Peking University)
The Mordell conjecture, proved by Faltings in 1983, asserts that there are only finitely many rational points on a curve of genus at least two over a number field. The uniform Mordell problem asks for suitable upper bounds on the number of rational points in the Mordell conjecture. In this talk, we will introduce various recent developments on this uniformity problem.
6:00 PM – 6:45 PM 121-AB Section Lecture

Ricci-Flat Metrics on Calabi-Yau Manifolds

  • Valentino Tosatti (Courant Institute of Mathematical Sciences, New York University)
I will give an introduction to Calabi-Yau manifolds and their Ricci-flat Kähler metrics. Given a Calabi-Yau manifold, I will then discuss the possible ways in which such metrics can degenerate, pose a number of questions, and present some recent results about these questions.

Thursday, July 30, 2026

9:00 AM – 10:00 AM Terrace Ballroom Plenary Lecture

Geometric Concepts in Partial Differential Equations

  • Felix Otto (Max Planck Institute for Mathematics in the Sciences, Leipzig)

Being intrigued by the use of intuition and concepts from differential and in particular Riemannian geometry in the infinite-dimensional set-ting of field equations, I’d like to sketch a couple of examples: 

  • The physics-informed interpretation of multi-phase flows in porous media – as gradient flows on the space of densities endowed with a metric from optimal transportation.
  • The renormalization of quasi-linear parabolic equations driven by noisy and thus rough right-hand sides – interpreted as the robust construction of canonical charts and transition maps for the solution manifold, with the help of derivatives with respect to the noise.
  • The connection between drift-diffusion equations with critical ensembles of divergence-free drifts in n-dimensional space – and the geometric Brownian motion on the Lie group Sl(n).
10:15 AM – 11:15 AM Terrace Ballroom Plenary Lecture

Quantitative Rectifiability and Harmonic Measure

  • Xavier Tolsa (ICREA, Autonomous University of Barcelona, and CRM)
A set in the Euclidean space is called n-rectifiable if it is almost all contained in a countable union of C1 n-dimensional manifolds. The theory of quantitative rectifiability studies this property using tools from harmonic analysis, such as square functions and singular integrals.On the other hand, harmonic measure is a fundamental notion in the solution of the Dirichlet problem for the Laplace equation and has important applications in complex analysis. For a bounded domain, the harmonic measure of a subset of the boundary coincides with the probability that a Brownian motion starting inside the domain exits the domain through that subset. An important and old problem in analysis consists in understanding the relationship between harmonic measure and surface measure in a given domain. The notion of rectifiability plays a central role in this problem. In this talk we will survey classical results and recent advances on this topic obtained using tools from quantititative rectifiability. In particular, we will describe the solution of the one-phase and two-phase problems for harmonic measure and new results about the solvability of the Dirichlet and regularity problems in rough domain in Lp.
11:30 AM – 1:00 PM Breaks

Lunch on Own

1:00 PM – 2:30 PM Terrace Ballroom Receptions & Special Events

Closing Ceremony