Calendar
Posted August 27, 2025
Last modified November 24, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett Hall 233
Huong Vo, Louisiana State University
Incoherence of free-by-free groups
A group is incoherent if it has a finitely generated subgroup that is not finitely presented. In this talk, we'll look at how an amalgamated product construction and a homological condition called excessive homology show incoherence of many free-by-free groups.
Posted November 30, 2025
Mathematical Physics and Representation Theory Seminar
12:00 pm – 1:00 pm Keisler Lounge (Room 321 Lockett)
Iain Moffatt, Royal Holloway, University of London
Graph Theory Graduate Student Q&A and Lunch
Bring your lunch to the third floor lounge to interact with Iain Moffatt before his talk (at 1:30pm). All are welcome--professors, students, postdocs--but this question and answer period is mainly for graduate students. Iain will speak about the basic objects of his talk--hypermaps. These are combinatorial structures that encode embeddings of (generalized) graphs on surfaces, and they appear naturally in areas ranging from topological graph theory to algebraic geometry and low-dimensional topology. In this informal session he will introduce hypermaps, draw plenty of pictures, and explain how they arise in current research. The goal is to build intuition for the main talk, so questions are encouraged and no prior background in hypermaps or surface embeddings will be assumed.
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
Last modified December 1, 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
Hypergeometric Motives and Modular Forms
We will discuss hypergeometric motives and their different aspects, which include classical hypergeometric functions and hypergeometric functions over finite fields. Using the Explicit Hypergeometric Modularity Method recently introduced by Allen, Grove, Long, and Tu, we also explain the relationship between certain special hypergeometric motives and modular forms.
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 November 30, 2025
Informal Analysis Seminar Questions or comments?
3:30 pm – 4:30 pm Lockett 136
Han Nguyen, LSU
Modelling and simulation of the cholesteric Landau-de Gennes model
This paper discusses modelling and numerical issues in the simulation of the Landau-de Gennes (LdG) model of nematic liquid crystals (LCs) with cholesteric effects. We propose a fully implicit, (weighted) L2 gradient flow for computing energy minimizers of the LdG model, and note a timestep restriction for the flow to be energy decreasing. Furthermore, we give a mesh size restriction, for finite-element discretizations, that is critical to avoid spurious numerical artifacts in discrete minimizers, particularly when simulating cholesteric LCs that exhibit ‘twist.’ Furthermore, we perform a computational exploration of the model and present several numerical simulations in three dimensions, on both slab geometries and spherical shells, with our finite-element method. The simulations are consistent with experiments, illustrate the richness of the cholesteric model, and demonstrate the importance of the mesh size restriction.
Posted September 10, 2025
Last modified December 2, 2025
Geometry and Topology Seminar Seminar website
1:30 pm Lockett 233
Corey Bregman, Tufts University
Diffeomorphism groups of reducible 3-manifolds
Let M be a smooth, compact, connected orientable 3-manifold. A classical result of Kneser and Milnor states that M admits a connected sum decomposition into prime factors, unique up to reordering. We introduce a topological poset of embedded 2-spheres in M and use it to study the classifying space BDiff(M) for the diffeomorphism group of M. We prove that if M is closed then BDiff(M) has finite type, and if M has non-empty boundary then BDiff(M rel ∂M) is homotopy equivalent to a finite CW complex. The proof will take us on crash course through classical 3-manifold topology and geometrization. This is joint work with Rachael Boyd and Jan Steinebrunner.
Posted August 27, 2025
Last modified November 26, 2025
Informal Geometry and Topology Seminar Questions or comments?
3:30 pm Lockett Hall 233
Krishnendu Kar, Louisiana State University
Khovanov Homology
Wrapping up our discussion on Khovanov Homology from this semester.
Posted November 13, 2025
Last modified December 3, 2025
Colloquium Questions or comments?
3:30 pm Zoom
Peter Bradshaw, University of Illinois Urbana-Champaign
Toward Vu's conjecture
In 2002, Vu conjectured that graphs of maximum degree $\Delta$ and maximum codegree at most $\zeta \Delta$ have chromatic number at most $(\zeta+o(1))\Delta$. Despite its importance, the conjecture has remained widely open. The only direct progress so far has been obtained in the "dense regime,'' when $\zeta$ is close to $1$, by Hurley, de Verclos, and Kang.
In this talk, I will discuss one of my recent results achieving the first major progress in the sparse regime where \zeta approaches 0, the case of primary interest to Vu. The result states that there exists $\zeta_0 > 0$ such that for all $\zeta \in [\log^{-32}\Delta,\zeta_0]$, the following holds: if $G$ is a graph with maximum degree $\Delta$ and maximum codegree at most $\zeta \Delta$, then $\chi(G) \leq (\zeta^{1/32} + o(1))\Delta$. This bound is derived from a more general result that assumes only that the common neighborhood of any $s$ vertices is bounded rather than the codegrees of pairs of vertices. The more general result also extends to the list coloring setting, which is of independent interest.
This talk is based on joint work with Dhawan, Methuku, and Wigal.
Posted December 3, 2025
Faculty Meeting Questions or comments?
12:00 pm ZoomMeeting of the Professorial Faculty
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 August 18, 2025
Last modified December 4, 2025
Control and Optimization Seminar Questions or comments?
10:30 am – 11:20 am Zoom (click here to join)
Zequn Zheng, Louisiana State University
Generating Polynomial and Optimization-Based Algorithms for Tensor Decomposition
Tensors, or multidimensional arrays, are higher-order generalizations of matrices that naturally represent data with inherent multi-way structure. Tensor rank decomposition is a key tool for uncovering hidden patterns in such data. In this talk, we introduce a novel algorithm based on generating polynomials to compute tensor decompositions. We prove that under certain rank conditions, our method recovers the exact decomposition. For higher ranks beyond this threshold, we provide an optimization-based variant that effectively detects the tensor decomposition. Numerical experiments illustrate the robustness and efficiency of our approach.
Posted December 2, 2025
Combinatorics Seminar Questions or comments?
2:30 pm – 3:30 pm Zoom (Click here to attend on Zoom)
Kevin Grace, University of South Alabama
Matroid Adjoints, Minors, and Matrix Patterns
The notion of an adjoint of a matroid M arises from the attempt to attach a matroid to the lattice-theoretic dual of the lattice of flats of M. More precisely, a simple matroid M’, with the same rank as M, is an adjoint of M if there is an inclusion-reversing injective map from the lattice of flats of M into the lattice of flats of M’ that bijectively maps the hyperplanes of M onto the points of M’. Not all matroids have adjoints; however, in this talk, I will present a proof that the class of matroids that do have adjoints is minor-closed. If time permits, I will also discuss related work from the field of combinatorial matrix theory. In this related work, joint with Louis Deaett, we explore connections between the notion of an adjoint of a matroid and the minimum rank of matrices with a given zero-nonzero pattern.
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 December 8, 2025
Faculty Meeting Questions or comments?
10:00 am ZoomMeeting of the Professorial Faculty
Posted December 8, 2025
Faculty Meeting Questions or comments?
9:30 am ZoomMeeting of the Professorial Faculty
Posted July 22, 2025
Last modified December 4, 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.