Analysis on simple Lie groups and lattices

Abstract

We present a simple tool to perform analysis with groups such as SL(n,R) and SL(n,Z), that has been introduced by Vincent Lafforgue in his study of non-unitary representations, in connection with the Baum-Connes conjecture and strong property (T). It has been later applied in various contexts: operator algebras, Fourier analysis, geometry of Banach spaces or dynamics. The idea is to first restrict to compact subgroups and then exploit how they sit inside the whole group.

Prepared for the proceedings of the ICM2022 (20 pages)