Speaker:   Roman Bezrukavnikov (MIT)

Where:      In-Person at MIT Room 2-135 and on

Zoom         https://mit.zoom.us/j/94469771032?pwd=d3JaSVhVV0xDOGpkUDdveXdOYmNXQT09

Title:  "Local L-factors and configuration spaces"

Abstract:  L-functions play a central role in the theory of automorphic forms and Langlands conjectures. In particular, the conjectures predict existence of certain functions of one variable, the so called local L-factors, assigned to an irreducible representation of a p-adic group G (with a bit of extra data) and a representation of the dual group. When G=GL(n) equipped with the standard n-dimensional representation of the dual group, such a construction was proposed by Godement and Jacquet in 1972.

In a joint work with Braverman, Finkelberg and Kazhdan we propose a generalization of that construction in the functional field case based on geometry of the global Grassmannian. The main result is that the construction produces the expected answer for representations of G generated by an Iwahori invariant vector, its proof is based on my earlier work on the categorification of the affine Hecke algebra and perverse coherent sheaves on the nilpotent cone.