Calendar

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Monday, November 24, 2025

Posted November 12, 2025
Last modified November 16, 2025

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.

Tuesday, November 25, 2025

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.

Wednesday, November 26, 2025

Posted August 27, 2025
Last modified November 21, 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.

Monday, December 1, 2025

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.

Tuesday, December 2, 2025

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.

Wednesday, December 3, 2025

Posted August 27, 2025
Last modified November 21, 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 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

Thursday, December 4, 2025

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.

Friday, December 5, 2025

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.

Friday, December 12, 2025

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

Friday, January 2, 2026

Posted November 5, 2025

Graduate Student Event

1:00 pm – 4:00 pm Lockett Hall 232

Qualifier Exam in Algebra

Event contact: Stephen Shipman

Monday, January 5, 2026