Calendar

Posted September 15, 2025

Combinatorics Seminar Questions or comments?

Rose McCarty, Georgia Institute of Technology
Neighborhood complexity and matroids

Abstract: We will discuss neighborhood complexity in graphs and some of its many applications. We will touch on applications to graph coloring, discrete geometry, and first-order logic. However, our main focus will be using neighborhood complexity to find the "unavoidable" GF(q)-representable cosimple matroids of large girth. This talk is based on joint work with James Davies, Meike Hatzel, Kolja Knauer, and Torsten Ueckerdt.

Posted August 2, 2025
Last modified September 10, 2025

Algebra and Number Theory Seminar Questions or comments?

Andreas Mono, Vanderbilt University
A modular framework for generalized Hurwitz class numbers

We discover a neat linear relation between the mock modular generating functions of the level $1$ and level $N$ Hurwitz class numbers. This relation gives rise to a holomorphic modular form of weight $\frac{3}{2}$ and level $4N$ for $N > 1$ odd and square-free. This follows from a more general inspection of the weight $\frac{1}{2}$ Maass–Eisenstein series of level $4N$v at its spectral point $s = \frac{3}{4}$. This idea goes back to Duke, Imamoğlu and Tóth in level $4$ and relies on the theory of so-called sesquiharmonic Maass forms. Furthermore, we connect the aforementioned results to a regularized Siegel theta lift as well as a regularized Kudla–Millson theta lift for odd prime levels, which builds on earlier work by Bruinier, Funke and Imamoğlu. This is joint work with Olivia Beckwith. We conclude by presenting the situation in higher weights as well, which is sole work.

Posted September 18, 2025

Informal Analysis Seminar Questions or comments?

Matthew McCoy, Louisiana State University
Introduction to Ergodic Theory, Chebyshev Polynomial Expansions, and Schur Complements

This talk will serve as an introductory talk to Ken Beard's talk on 9/30: Momentum Space Algorithm for Electronic Structure of Double-Incommensurate Trilayer Graphene. We will introduce relevant concepts in spectral theory.

Event contact: Laura Kurtz

Posted September 1, 2025
Last modified September 18, 2025

Geometry and Topology Seminar Seminar website

Robin Koytcheff, University of Louisiana, Lafayette
Milnor invariants and thickness of spherical links

Various authors have studied the question of how long a rope of a given thickness is needed to tie a given isotopy class of knot or link.  In joint work with Rafal Komendarczyk and Fedya Manin, we generalize this work to spherical links in arbitrary dimensions.  In more detail, we study their Milnor invariants in terms of Massey products and prove asymptotically optimal upper bounds on Milnor invariants in terms of embedding thickness.  Interestingly, there is a dichotomy between polynomial and exponential bounds, depending on the dimensions of the spheres.  We apply our results to answer a question of Freedman and Krushkal about exponentially thin 2-complexes in 4-space.

Posted August 27, 2025

Informal Geometry and Topology Seminar Questions or comments?

Gargi Patil, Louisiana State University
TBD

TBD