# Geometric local Langlands correspondence and the (stable) Bernstein center

SPEAKER: Yakov Varshavsky

TITLE: Geometric local Langlands correspondence and the (stable) Bernstein center

ABSTRACT: This is part of the joint project in progress with Roman Bezrukavnikov and David Kazhdan. The goal of the project is to develop a geometric local Langlands correspondence in the $ell$-adic setting and apply it to the classical Langlands correspondence in general, and to the study of the (stable) Bernstein center, in particular. To illustrate the general picture, I will explain how to provide a geometric construction of the Bernstein projector to the depth zero spectrum. As an application, I will give its explicit formula and show its stability. In the first lecture I will formulate a version of the local Langlands correspondence, called the stable center conjecture, state our main result and outline strategy of the proof. Then, in the second lecture, I will sketch the proof