# Colloquium: Y. Varshavsky (HUJI)

Date:
Thu, 03/11/202214:30-15:30
Title: Geometric Langlands correspondence in the ell-adic setting

Abstract: The famous Langlands conjecture asserts that there is a correspondence between so-called automorphic representations" and Galois representations".

In his remarkable work Vincent Lafforgue proved the from automorphic to Galois" direction of the global Langlands conjecture over function fields. In order to do it he constructed a decomposition of the space of (cuspidal) automorphic forms, parameterized by semi-simple Langlands parameters for the Langlands dual group.

In the first part of the talk, I will discuss the global Langlands conjectures over the function fields, and describe Vincent Lafforgue's result.

In the second part of the talk I will discuss a categorification'' of Lafforgue's result, from which (among other things) the (unramified case of) of Lafforgue's result follows.

This is a joint project with D. Arinkin, D. Gaitsgory, D. Kazhdan, S. Raskin and N. Rozenblyum.

Recording will be available at: https://huji.cloud.panopto.eu/Panopto/Pages/Sessions/List.aspx?folderID=a6e6beab-eb0e-47c6-9d5d-aeb500acb5ad