Week of January 30, 2022

January 31, 2022
Geometry, Symmetry and Physics On Bessel functions for representations of finite general linear groups 4:30pm -

Abstract: In the 60s, Gel'fand defined a Bessel function associated with irreducible generic representations of GL(n, F_q). The Bessel function plays an important role in the representation theory of GL(n, F_q), and served as a key ingredient in the proof of the finite field analog of Jacquet's conjecture. However, the computation of explicit values of the Bessel function is difficult. In this talk, I'll explain a method based on gamma factors to compute values of the Bessel function. I will also explain a relation between some values of the Bessel function and Katz's generalized Kloosterman sheaves.

February 1, 2022
Algebra and Number Theory Seminar The K-theory of monoid sets 4:30pm -

Monoid sets are a non-additive model for toric varieties and offer a different avenue of exploration of that theory. I will give the definition of a monoid set, some key examples, and define their K-theory. We then prove that the K-theory of monoid sets satisfies analogous properties to the K-theory of algebraic (or toric) varieties, principal among them a localization theorem. Time permitting, I will do a calculation. This work is joint with Charles Weibel.

February 3, 2022
Algebra and Geometry lecture series An informal introduction to categorical actions of groups, Lecture 1 4:00pm -
February 4, 2022
Friday Mornings Friday Morning Seminar 9:00am -

We discussĀ topics of common interest in the areas of geometry, probability, and combinatorics.

Geometric Analysis and Application L^p-stability and positive scalar curvature rigidity of Ricci-flat ALE manifolds 2:00pm -


We prove stability of integrable ALE manifolds with a parallel spinor under Ricci flow, given an initial metric which is close in $L^p\cap L^{\infty}$, for any $p\in (1,n)$, where n is the dimension of the manifold. In particular, our result applies to all known examples of 4-dimensional gravitational instantons. The result is obtained by a fixed point argument, based on novel estimates for the heat kernel of the Lichnerowicz Laplacian. It allows us to give a precise description of the convergence behaviour of the Ricci flow. Our decay rates are strong enough to prove positive scalar curvature rigidity in $L^p$, for each $p\in [1,\frac{n}{n-2})$, generalizing a result by Appleton. This is joint work with Oliver Lindblad Petersen.