Calendar

Posted December 3, 2025

Faculty Meeting Questions or comments?

Meeting of the Professorial Faculty

Posted November 12, 2025

Colloquium Questions or comments?

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?

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?

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?

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.