Analysis on homogeneous spaces and operator algebras

Reductive groups and C∗-algebras: why and how

24 mars 2025, 09:30

1h

Amphithéâtre Hermite (Institut Henri Poincaré)

Orateur

Alexandre Afgoustidis (CNRS & Institut Élie Cartan de Lorraine)

Description

This talk is a review of aspects, old and new, of the connection between harmonic analysis on real reductive groups and the structure of certain $C^{\ast }$-algebras attached to them.
Topics will include the topology of the tempered dual, the Baum--Connes--Kasparov conjecture in K-theory, and the Mackey bijection between the tempered dual of a real reductive group and the unitary dual of its Cartan motion group.
The talk is intended to serve as an introduction to work in progress on similar questions for harmonic analysis on symmetric spaces. I will discuss what happens when one views the group as a symmetric space in this context. Later in the week, Shintaro Nishikawa will talk about some of our joint work, also joint with Nigel Higson, Peter Hochs and Yanli Song, about $C^{\ast }$-algebras for other symmetric spaces.