Calendar
Posted November 5, 2025
Last modified November 17, 2025
Geometry and Topology Seminar Seminar website
1:30 pm Online
Advika Rajapakse, UCLA
Four Steenrod squares on Khovanov homology
The odd Khovanov spectrum is a space-level link invariant that, after taking (reduced) cohomology, recovers odd Khovanov cohomology. We use the second Steenrod square to disprove several conjectures regarding the odd Khovanov spectrum. We furthermore prove that there exists more than one even Khovanov spectrum, answering another question from Sarkar-Scaduto-Stoffregen.
Posted August 27, 2025
Last modified November 17, 2025
Informal Geometry and Topology Seminar Questions or comments?
3:30 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
Last modified November 16, 2025
Colloquium Questions or comments?
3:30 pm 232 Lockett Hall
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 16, 2025
Colloquium Questions or comments?
3:30 pm 232 Lockett Hall
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 18, 2025
Combinatorics Seminar Questions or comments?
2:30 pm – 3:30 pm Zoom
Jake Weber, Louisiana State University
Characterizations of Graph Classes between Claw-free Graphs and Line Graphs of Multigraphs
A line graph $L(G)$ of $G = (V, E)$ is the graph with vertex set E in which $x, y \in E$ are adjacent as vertices if and only if they are adjacent as edges in G. In 1970, Beineke (and Robertson independently) discovered a forbidden induced subgraph characterization for the class of line graphs of simple graphs. Bermond and Meyer in 1973 generalized this characterization to the class of line graphs of multigraphs, denoted $\mathcal{L}$. One such obstruction of these classes is $K_{1,3},$ the claw. In 2008, Chudnovsky and Seymour fully characterized the set of claw-free graphs. In this talk, we present constructive characterizations of classes between $\mathcal{L}$ and claw-free graphs. These constructions aim to provide an alternative approach, with fewer graph classes and operations, to that of Chudnovsky and Seymour. This talk is based on joint work with Guoli Ding.
Posted November 12, 2025
Last modified November 16, 2025
Colloquium Questions or comments?
3:30 pm 232 Lockett Hall
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 16, 2025
Colloquium Questions or comments?
4:00 pm 232 Lockett Hall
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 16, 2025
Colloquium Questions or comments?
3:30 pm 232 Lockett Hall
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
Last modified November 17, 2025
Colloquium Questions or comments?
3:30 pm 232 Lockett Hall
Mengxuan Yang, Princeton University
Flat bands in 2D materials
Magic angles are a hot topic in condensed matter physics: when two sheets of graphene are twisted by these angles, the resulting material is superconducting and the so-called energy bands are flat and topological. In 2011, Bistritzer and MacDonald proposed a model that is experimentally very accurate in predicting magic angles. In this talk, I will introduce some recent mathematical progress on the Bistritzer--MacDonald's model, including the mathematical characterization of magic angles and flat bands, the generic existence of Dirac cones and how topological phase transitions occur at magic angles. I will also discuss some new mathematical discoveries in twisted multilayer graphene.
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
Last modified November 16, 2025
Colloquium Questions or comments?
3:30 pm 232 Lockett Hall
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 16, 2025
Colloquium Questions or comments?
3:30 pm 232 Lockett Hall
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 5, 2025
1:00 pm – 4:00 pm Lockett Hall 232Qualifier Exam in Algebra
Event contact: Stephen Shipman
Posted November 5, 2025
1:00 pm – 4:00 pm Lockett Hall 232Qualifier Exam in Analysis
Event contact: Stephen Shipman
Posted November 5, 2025
1:00 pm – 4:00 pm Lockett Hall 232Qualifier Exam in Topology
Event contact: Stephen Shipman
Posted November 5, 2025
1:00 pm – 4:00 pm Lockett Hall 232Qualifier Exam in Applied Math
Event contact: Stephen Shipman
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 September 3, 2025
1:00 pm – 4:00 pm Saturday, March 7, 2026 Digital Media Center TheatreScientific Computing Around Louisiana (SCALA) 2026
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