%0 Unpublished work
%T Analysis on simple Lie groups and lattices
%+ Institut Camille Jordan (ICJ)
%A de la Salle, Mikael
%Z Prepared for the proceedings of the ICM2022 (20 pages)
%8 2022-11-25
%D 2022
%Z 2204.12381
%Z Mathematics [math]/Functional Analysis [math.FA]
%Z Mathematics [math]/Group Theory [math.GR]
%Z Mathematics [math]/Operator Algebras [math.OA]Preprints, Working Papers, ...
%X 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.
%G English
%L hal-03872222
%U https://cnrs.hal.science/hal-03872222
%~ UNIV-ST-ETIENNE
%~ CNRS
%~ UNIV-LYON1
%~ INSA-LYON
%~ EC-LYON
%~ INSMI
%~ INSA-GROUPE
%~ UDL
%~ UNIV-LYON
%~ ANR