Calendar
Posted October 15, 2025
Last modified October 16, 2025
Mathematical Physics and Representation Theory Seminar
1:30 pm – 2:20 pm Lockett 233
Paul Sobaje, Georgia Southern University
A Geometric Model For Steinberg Quotients
Let G be a reductive algebraic group over a field of characteristic p > 0. Over the last decade, the longstanding search for a character formula for simple G-modules has been replaced (subsumed even) by the same problem for characters of tilting G-modules. In recent years I began studying "Steinberg quotients" of certain tilting characters. These are formal characters with good combinatorial properties straightforwardly derived from the representation theory of G. In some ways they are also the best candidates to be described by a characteristic p version of Weyl's famous formula. In joint work with P. Achar, we prove that these formal characters are in fact actual characters of a natural class of objects coming from geometric representation theory.
Posted November 12, 2025
Last modified November 14, 2025
Colloquium Questions or comments?
4:00 pm
Quanjun Lang, Duke University
Low-Rank Methods for Multitype Interacting Particle Systems and Quantum Superoperator Learning
We introduce a multi-type interacting particle system on graphs to model heterogeneous agent-based dynamics. Within this framework, we develop algorithms that jointly learn the interaction kernels, the latent type assignments, and the underlying graph structure. The approach has two stages: (i) a low-rank matrix sensing step that recovers a shared interaction embedding, and (ii) a clustering step that identifies the discrete types. Under the assumption of the restricted isometry property (RIP), we obtain theoretical guarantees on sample complexity and convergence for a wide range of model parameters. Building on the same low-rank matrix sensing framework, I will then discuss quantum superoperator learning, encompassing both quantum channels and Lindbladian generators. We propose an efficient randomized measurement design and use accelerated alternating least squares to estimate the low-rank superoperator. The resulting performance guarantees follow from RIP conditions, which are known to hold for Pauli measurement ensembles.
Posted November 15, 2025
Algebra and Number Theory Seminar Questions or comments?
2:00 pm – 3:00 pm Lockett 233 or click here to attend on Zoom
Jiaqi Hou, Louisiana State University
Restriction bounds for Maass forms
I will talk about the analytic problem of bounding Hecke–Maass forms. From the general theory of bounding Laplace eigenfunctions on Riemannian manifolds, one obtains local bounds for many different kinds of norms, and these bounds are believed to be far from optimal if the manifold is negatively curved. I will discuss how Hecke–Maass forms on arithmetic hyperbolic 3-folds behave along totally geodesic surfaces and present an improved L^2 bound by the method of arithmetic amplification.
Posted November 15, 2025
Algebra and Number Theory Seminar Questions or comments?
2:00 pm – 3:00 pm Lockett 233 or click here to attend on ZoomRestriction bounds for Maass forms
I will talk about the analytic problem of bounding Hecke-Maass forms. From the general theory of bounding Laplace eigenfunctions on Riemannian manifolds, one obtains local bounds for many different kinds of norms, and these bounds are believed to be far from optimal if the manifold is negatively curved. I will discuss how Hecke-Maass forms on arithmetic hyperbolic 3-folds behave along totally geodesic surfaces and present an improved L^2 bound by the method of arithmetic amplification.
Posted November 3, 2025
Last modified November 10, 2025
Computational Mathematics Seminar
3:30 pm – 4:30 pm Digital Media Center 1034
Jai Tushar, Louisiana State University
Recent Advances in Polytopal Finite Element Methods with Application to Domain Decomposition Methods
Polytopal finite element methods (FEMs) have gained popularity in recent years due to their ability to relax conformity constraints on meshes. This flexibility makes them well-suited for handling complex geometries, adaptive mesh refinement, and coarsening. The design of efficient, robust, scalable solvers for linear systems arising from these kinds of discretizations is important to make them competitive with traditional methods. Non-overlapping domain decomposition methods (DDMs) provide one such family of pre-conditioners. In this talk we first give a heuristic answer to “Why polytopal FEMs?” We then outline several routes from traditional conforming FEMs to polytopal formulations. Next, we present recent tools—rooted in discrete functional analysis and mimicing the continuous setting—that yield condition-number estimates for non-overlapping DDM pre-conditioners arising from these discretizations. Finally, we show robustness and scalability of our pre-conditioner for up to several hundreds of processors performed using the open-source finite element library Gridap.jl.
Posted November 5, 2025
3:30 pm Lockett 276
Paul Sobaje, Georgia Southern University
Affine Group Schemes and Frobenius Kernels
We will give an introduction to affine group schemes over a field k from the viewpoint of k-group functors. These objects generalize the notion of an affine algebraic group over k. One of the most important examples of affine group schemes that are not algebraic groups come from the Frobenius kernels of algebraic groups in characteristic p > 0. We will discuss these objects and, time permitting, their representation theory.
Posted November 13, 2025
Informal Analysis Seminar Questions or comments?
3:30 pm – 4:30 pm Room 136
Anan Saha, LSU
Learning of Stochastic Differential Equations with integral-drift
Stochastic differential equations (SDEs) with integral drift arise naturally in multiscale systems and in applications where effective dynamics are obtained by averaging over latent or unobserved processes. In such settings, the drift takes the form b̅(x) = ∫ b(x, y) π(dy), with π an unknown probability measure. Our primary goal is the nonparametric estimation of the averaged drift b̅ directly from observable data on X, thereby bypassing the need to recover the unidentifiable measure π, which is of secondary importance for understanding the dynamics of these types of SDE models. In this paper, we develop a nonparametric Bayesian framework for estimating b̅ based on L´evy process priors, which represent π via random discrete supports and weights. This induces a flexible prior on the drift function while preserving its structural relationship to b(x, y). Posterior inference is carried out using a reversible-jump Hamiltonian Monte Carlo (RJHMC) algorithm, which combines the efficiency of Hamiltonian dynamics with transdimensional moves needed to explore random support sizes. We evaluate the methodology on multiple SDE models, demonstrating accurate drift recovery, consistency with stationary distributions, and robustness under different data-generating mechanisms. The framework provides a principled and computationally feasible approach for estimating averaged dynamics in SDEs with integral drift.
Event contact: Laura Kurtz
Posted November 5, 2025
Geometry and Topology Seminar Seminar website
1:30 pm Online
Advika Rajapakse, UCLA
TBA
Posted August 27, 2025
Last modified October 27, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett Hall 233
Nilangshu Bhattacharyya, Louisiana State University
Khovanov Homology
Continuing our discussion of Khovanov Homology following Melissa Zhang's notes.
Posted November 14, 2025
Colloquium Questions or comments?
3:30 pm
Aaron Calderon, University of Chicago
Pants decompositions and dynamics on moduli spaces
Every closed hyperbolic surface X (or Riemann surface or smooth algebraic curve over C) can be described by gluing together pairs of pants (three-holed spheres). Each X can be glued out of pants in many different ways, and Mirzakhani showed that the count of these decompositions is closely related to a certain Hamiltonian flow on the moduli space of hyperbolic surfaces. In the field of Teichmüller dynamics, counting problems on flat surfaces can be related to a different dynamical system on a different moduli space, which, by work of Eskin--Mirzakhani--Mohammadi and Filip, is in turn controlled by special algebraic subvarieties. In this talk, I will survey some of these results and describe a bridge between the two worlds that can be used to transfer theorems between flat and hyperbolic geometry.
Posted November 12, 2025
Last modified November 13, 2025
Colloquium Questions or comments?
3:30 pm
Benjamin Zhang, University of North Carolina at Chapel Hill
A mean-field games laboratory for generative artificial intelligence: from foundations to applications in scientific computing
We demonstrate the versatility of mean-field games (MFGs) as a mathematical framework for explaining, enhancing, and designing generative models. We establish connections between MFGs and major classes of flow- and diffusion-based generative models by deriving continuous-time normalizing flows and score-based models through different choices of particle dynamics and cost functions. We study the mathematical structure and properties of each generative model by examining their associated MFG optimality conditions, which consist of coupled forward-backward nonlinear partial differential equations (PDEs). We present this framework as an MFG laboratory, a platform for experimentation, invention, and analysis of generative models. Through this laboratory, we show how MFG structure informs new normalizing flows that robustly learn data distributions supported on low-dimensional manifolds. In particular, we show that Wasserstein proximal regularizations inform the well-posedness and robustness of generative flows for singular measures, enabling stable training with less data and without specialized architectures. We then apply these principled generative models to operator learning, where the goal is to learn solution operators of differential equations. We present a probabilistic framework that reveals certain classes of operator learning approaches, such as in-context operator networks (ICON), as implicitly performing Bayesian inference. ICON computes the mean of the posterior predictive distribution of solution operators conditioned on example condition-solution pairs. By extending ICON to a generative setting, we enable sampling from the posterior predictive distribution. This provides principled uncertainty quantification for predicted solutions, demonstrating how mathematical foundations translate to trustworthy applications in scientific computing.
Posted July 13, 2025
Last modified November 4, 2025
Control and Optimization Seminar Questions or comments?
10:30 am – 11:20 am Zoom (click here to join)
Dimitra Panagou, University of Michigan
AFOSR YIP, NASA Early Career Faculty, and NSF CAREER Awardee
Safety-Critical Control via Control Barrier Functions: Theory and Applications
This seminar will focus on control barrier functions, as a tool for encoding and enforcing safety specifications, as well as their recent extensions (e.g., robust, adaptive, and predictive) to handle additive perturbations, parametric uncertainty and dynamic environments, with applications to (multi)-robot/vehicle motion planning and coordination. Time permitting, we will also cover how time constraints can be encoded as fixed-time control Lyapunov functions, and the trade-offs between safety and timed convergence.
Posted November 12, 2025
Colloquium Questions or comments?
3:30 pm
Colleen Robichaux, University of California, Los Angeles
Deciding Schubert positivity
We survey the study of structure constants in Schubert calculus and its connection to combinatorics and computational complexity.
Posted November 12, 2025
Last modified November 14, 2025
Colloquium Questions or comments?
4:00 pm
Keegan Kirk, George Mason University
Nonsmooth Variational Problems, Optimal Insulation, and Digital Twins
How should a fixed amount of insulating material be placed on a heat-conducting body to maximize thermal performance? A thin-shell model of the insulating layer yields, through rigorous asymptotic analysis, a convex but nonsmooth, nonlocal variational problem. To handle the resulting nonsmooth terms, we develop an equivalent Fenchel-dual formulation together with a semi-smooth Newton method built on the discrete duality inherited by Raviart–Thomas and Crouzeix–Raviart elements. We establish a priori and a posteriori error estimates and validate the theory through numerical experiments, including optimal home insulation and spacecraft heat shielding. Beyond its intrinsic mathematical interest, this problem serves as a building block for digital twins, virtual replicas of physical systems that incorporate sensor data and quantify uncertainty to inform decisions about their physical counterparts. One concrete example arises in the refurbishment of a spacecraft’s heat shield after atmospheric re-entry, where available data can be used to infer how much insulation remains on the surface. The model could then optimize where and how much new material to add, under uncertainty about the residual thickness and anticipated thermal loads. The outcome is a high-dimensional, nonsmooth variational problem representative of the optimal control tasks encountered in digital twin settings. The efficient numerical solution of these high-dimensional optimal control problems remains a formidable challenge for the widespread deployment of digital twins. We therefore highlight two complementary research directions aimed at reducing the computational burden: (i) structure aware preconditioning strategies for nonsmooth optimal control problems, including applications to neural network training, and (ii) adaptive tensor-decomposition techniques that enable efficient approximation of high-dimensional stochastic variational problems.
Posted November 3, 2025
Last modified November 9, 2025
Computational Mathematics Seminar
3:30 pm – 4:30 pm Digital Media Center 1034
Monika Pandey, Louisiana State University
Adaptive proximal Barzilai–Borwein method for nonlinear optimization
In this presentation, I will discuss adaptive proximal algorithms that builds on the Barzilai–Borwein (BB) stepsize strategy to accelerate gradient-based methods for solving nonlinear composite optimization. For convex problems, we design adaptive rules that automatically adjust the stepsizes using local curvature information, removing the need for traditional line searches, and enhancing both robustness and computational efficiency. These ideas are further extended to nonconvex problems by developing a new nonmonotone line search strategy that preserves global convergence. I will present theoretical guarantees and numerical experiments showing that the proposed Adaptive Proximal Barzilai–Borwein (AdProxBB) method achieves faster convergence and stronger performance than existing proximal gradient algorithms.
Posted August 27, 2025
Last modified October 27, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett Hall 233
Huong Vo, Louisiana State University
TBD (Independent Talk)
TBD (Independent Talk)
Posted November 12, 2025
Mathematical Physics and Representation Theory Seminar
1:30 pm – 2:20 pm Lockett 233
Iain Moffatt, Royal Holloway, University of London
Hypermap minors
As mathematicians we conventionally model networks as graphs. In a graph, each edge has exactly two ends, each lying on a vertex. Hypergraphs generalise graphs by allowing an edge to have any number of ends. As the edges of a hypergraph can connect any number of vertices, not just two, they offer a way to model higher-order interactions in networks. Graphs often arise in applications with the additional structure of an embedding in a surface. This is also happens for hypergraphs: a hypermap is a hypergraph embedded in a closed surface. This talk is about hypermaps. I'll begin by reviewing the basics of hypermaps, including various ways to describe them. I'll go on to present a theory of hypermap minors based upon a smoothing operation in cubic graphs. I'll discuss various aspect of this theory such as commutativity, duality and Tutte's triality, polynomials, and relations with Farr's theory of alternating dimaps. This is joint work with Jo Ellis-Monaghan and Steven D. Noble.
Posted November 13, 2025
Last modified November 14, 2025
Colloquium Questions or comments?
3:30 pm
Sky Cao, Massachusetts Institute of Technology
Yang-Mills, probability, and stochastic PDE
Originating in physics, Yang-Mills theory has shaped many areas of modern mathematics. In my talk, I will present Yang-Mills theory in the context of probability, highlighting central questions and recent advances. In particular, I will discuss the role of stochastic partial differential equations (SPDEs) in these developments and survey some of the recent progress in this field.
Posted November 15, 2025
Algebra and Number Theory Seminar Questions or comments?
2:00 pm – 3:00 pm Lockett 233 or click here to attend on Zoom
Esme Rosen, Louisiana State University
TBA
TBA
Posted November 13, 2025
Colloquium Questions or comments?
3:30 pm
Mengxuan Yang, Princeton University
To be announced
Posted August 27, 2025
Last modified October 27, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett Hall 233
Krishnendu Kar, Louisiana State University
Khovanov Homology
Wrapping up our discussion on Khovanov Homology from this semester.
Posted September 10, 2025
Last modified September 23, 2025
Geometry and Topology Seminar Seminar website
3:30 pm Lockett 233
Corey Bregman, Tufts University
TBA
TBA
Posted November 13, 2025
Colloquium Questions or comments?
3:30 pm
Peter Bradshaw, University of Illinois Urbana-Champaign
To be announced
Posted November 12, 2025
Colloquium Questions or comments?
3:30 pm Lockett 232
Iain Moffatt, Royal Holloway, University of London
Graphs in surfaces, their one-face subgraphs, and the critical group
Critical groups are groups associated with graphs. They are well-established in combinatorics; closely related to the graph Laplacian and arising in several contexts such as chip firing and parking functions. The critical group of a graph is finite and Abelian, and its order is the number of spanning trees in the graph, a fact equivalent to Kirchhoff’s Matrix--Tree Theorem.
What happens if we want to define critical groups for graphs embedded in surfaces, rather than for graphs in the abstract?
In this talk I'll offer an answer to this question. I'll describe an analogue of the critical group for an embedded graph. We'll see how it relates to the classical critical groups, as well as to Chumtov's partial-duals, Bouchet's delta-matroids, and a Matrix--quasi-Tree Theorem of Macris and Pule, and describe how it arises through a chip-firing process on graphs in surfaces.
This is joint work with Criel Merino and Steven D. Noble.
Posted July 22, 2025
Last modified November 13, 2025
Control and Optimization Seminar Questions or comments?
10:30 am – 11:20 am Zoom (click here to join)
Javad Velni, Clemson University
Optimal Supplemental Lighting in Controlled Environment Agriculture: Data-driven and Model-based Perspectives
This seminar presents one aspect of my lab’s research focused on developing optimal supplemental lighting control strategies using LED lamps in controlled environment agriculture. The work aims to minimize electricity costs associated with supplemental lighting by integrating model-based optimization techniques with advanced machine learning methods, such as deep neural networks and Markov chains, used to predict uncertain environmental variables. Several scenarios are explored, ranging from a baseline optimal lighting approach for a single crop to more complex settings involving large-scale greenhouses with multiple crops and spatial light distribution considerations. Experimental results from a research greenhouse, where an Internet of Agricultural Things (IoAT) system was developed to grow lettuce, are presented and discussed. The seminar concludes with a roadmap highlighting several emerging research directions inspired by these findings.
Posted November 13, 2025
Last modified November 14, 2025
Colloquium Questions or comments?
3:30 pm
Sean Cotner, University of Michigan
Propagating congruences in the local Langlands program
The Langlands program is a vast generalization of quadratic reciprocity, aimed at understanding the algebraic field extensions of the rational or p-adic numbers. In this talk, I will describe a biased and incomplete history of the classical local Langlands program; recent developments in making it categorical, integral, and modular; and joint work-in-progress with Tony Feng concerned with patching together the modular theory to understand the classical theory.
Posted August 18, 2025
Control and Optimization Seminar Questions or comments?
10:30 am – 11:20 am Zoom (click here to join)
Zequn Zheng, Louisiana State University
TBA
Posted November 15, 2025
Algebra and Number Theory Seminar Questions or comments?
2:00 pm – 3:00 pm Lockett 233 or click here to attend on Zoom
Olivia Beckwith, Tulane University
TBA
TBA
Posted November 15, 2025
Algebra and Number Theory Seminar Questions or comments?
2:00 pm – 3:00 pm Lockett 233 or click here to attend on Zoom
Marco Sangiovanni Vincentelli, Columbia University
TBA
TBA
Posted November 15, 2025
Algebra and Number Theory Seminar Questions or comments?
2:00 pm – 3:00 pm Lockett 233 or click here to attend on Zoom
Kiran Kedlaya, University of California, San Diego
TBA
TBA