Invariant Distributions and Sheaves on Loop Groups

Résumé

I will present a version of the local Langlands conjecture providing a description of the space of invariant distributions on the p-adic group in terms of the K-group of coherent sheaves on the stack of Langlands parameters. This provides a description of invariant distributions that should correspond to character sheaves on the loop group. I will explain a few special cases understood in some detail: generic depth zero L-packet studied in a joint work with Varshavsky and unipotent case which is the subject of a joint work in progress with Ciubotaru, Kazhdan and Varshavsky. Time permitting, I will mention a joint work with Charlotte Chan which is the first step towards working out some higher depth cases.

Roman Bezrukavnikov

I received my PhD from Tel Aviv University in 1998, having also studied at Moscow State University and Brandeis University. After holding postdoctoral and assistant professor positions at Princeton IAS, the University of Chicago and Northwestern University, as well as a long term Clay Institute fellowship, I started a faculty appointment at MIT in 2005. My visiting appointments include an FSMP Chair in Paris in 2021.