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

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. 
Algebra and Number Theory Seminar  The Ktheory of monoid sets  4:30pm  
Monoid sets are a nonadditive 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 Ktheory. We then prove that the Ktheory of monoid sets satisfies analogous properties to the Ktheory 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. 
Algebra and Geometry lecture series  An informal introduction to categorical actions of groups, Lecture 1 
4:00pm 
https://yale.zoom.us/j/92613729337

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^pstability and positive scalar curvature rigidity of Ricciflat ALE manifolds  2:00pm  
Abstract: 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 4dimensional 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 $p\in [1,\frac{n}{n2})$, generalizing a result by Appleton. This is joint work with Oliver Lindblad Petersen. 