Calendar

Posted October 3, 2025
Last modified October 8, 2025

LSU SIAM Student Chapter

A Conversation with SIAM President

The SIAM Student Chapter and AWM Student Chapter are excited to host a Special Q and A session with the President of SIAM. This event provides students with an opportunity to directly engage with the President, ask questions, and gain insights into the world of Applied Mathematics and Computational Science. Refreshments will be provided.

Event contact: Gowri Priya Sunkara and Laura Kurtz

Posted August 2, 2025
Last modified October 8, 2025

Algebra and Number Theory Seminar Questions or comments?

Kenz Kallal, Princeton University
Algebraic theory of indefinite theta functions

Jacobi's theta function $\Theta(q) := 1 + 2q + 2q^4 + 2q^9 + \cdots $, and more generally the theta functions associated to positive-definite quadratic forms, have the property that they are modular forms of half-integral weight. The usual proof of this fact is completely analytic in nature, using the Poisson summation formula. However, $\Theta$ was originally invented by Fourier (Théorie analytique de la chaleur, 1822) for the purpose of studying the diffusion of heat on a uniform circle-shaped material: it is the fundamental solution to the heat equation on a circle. By algebraically characterizing the heat equation as a specific flat connection on a certain bundle on a modular curve, we produce a completely algebraic technique for proving modularity of theta functions. More specifically, we produce a refinement of the algebraic theory of theta functions due to Moret-Bailly, Faltings–Chai, and Candelori. As a consequence of the algebraic nature of our theory and the fact that it applies to indefinite quadratic forms / non-ample line bundles (which the prior algebraic theory does not), we also generalize the Kudla–Millson analytic theory of theta functions for indefinite quadratic forms to the case of torsion coefficients. This is joint work in progress with Akshay Venkatesh.

Posted October 10, 2025

Informal Analysis Seminar Questions or comments?

Long Teng, LSU
Nodal Sets of Harmonic Functions

In this talk, we study the size of nodal sets of harmonic functions. We introduce the frequency function N(r), which quantifies the growth rate of a harmonic function and plays a crucial role in understanding its zero set. I will first define this frequency function and show its monotonicity property. Then, using this tool, we establish that the (n−1)-dimensional Hausdorff measure of the nodal set is bounded above by C(n)N, where C(n) depends only on the dimension. This result highlights how quantitative unique continuation connects analytic growth properties of harmonic functions to the geometric complexity of their nodal sets.

Event contact: Laura Kurtz

Posted August 27, 2025

Informal Geometry and Topology Seminar Questions or comments?

Adithyan Pandikkadan, Louisiana State University
TBD

TBD

Posted September 10, 2025

Harmonic Analysis Seminar

Bruno Poggi, University of Pittsburgh
TBA

Posted September 26, 2025

Geometry and Topology Seminar Seminar website

Naageswaran Manikandan, Max Planck Institute
TBA

Posted October 6, 2025

Mathematical Physics and Representation Theory Seminar

John O'Brien, Louisiana State University
The Splitting-Rank Derived Satake Equivalence

This talk is based on joint work with Tsao-Hsien Chen, Mark Macerato, and David Nadler. We discuss a generalization of Bezrukavnikov-Finkelberg's Derived Satake Equivalence from complex reductive groups to certain real reductive groups--or equivalently, from compact Lie groups to the corresponding symmetric spaces. We use Nadler's Real Geometric Satake to compute the equivariant cohomology of the based loop space of a splitting-rank symmetric space, then use Achar's parity-vanishing machinery to establish the equivalence of derived categories.

Posted August 27, 2025
Last modified September 12, 2025

Applied Analysis Seminar Questions or comments?

Xuenan Li, Columbia University
TBA: Something on 2D electronic materials

Event contact: Stephen Shipman