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