Deformation theory of the Lafforgue variety - part 2

Abstract: In this series of talks we will construct the Lafforgue variety, an affine scheme equipped with an open dense subscheme parametrizing the simple modules of a non-commutative algebra that is a finite module over a finitely generated center. Our main applications and source of examples will be in the theory of Hecke algebras. We will also study how the Lafforgue variety varies under deformation of algebras, and in particular we prove in the case the center is regular a conjecture stated by Aubert, Baum and Plymen in 2007 on the reducibility loci of affine Hecke algebras.

In the first talk, we will introduce Hecke algebras and the type of questions we will consider, as well as relevant algebraic geometric notions for the second talk. In the second talk, we will construct the Lafforgue variety and study its deformation theory (the latter is work in progress).

Mathematics

Audience: researchers in the topic

Greek Algebra & Number Theory Seminar