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 $C$-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 $C*$-algebras for other symmetric spaces.
By Shintaro Nishikawa
By Juliette Coutens
By Yiannis Sakellaridis
By Bernhard Krötz
By Yoshiki Oshima
By Yiannis Sakellaridis
By Bernhard Krötz
By Polyxeni Spilioti
By Alain Connes
By Karl-Hermann Neeb
By Karl-Hermann Neeb
