The research school is an introductory meeting to the thematic program “Representation Theory and Noncommutative Geometry” to be held at IHP from January to March 2025. The trimester is part of an ongoing effort to bridge two fiels of Mathematics : the representation theory of locally compact groups and the theory of operator algebras. These research domains share origins in harmonic analysis, spectral theory and quantum mechanics but grew in separate directions. Recent progress in representation theory, involving especially non-Riemannian symmetric spaces and spherical varieties, and new tools developed in operator algebras, especially those involving K-theory and the other methods of non-commutative geometry, offer exciting prospects for new work at the interface between the two fields.

Mini-course are:

• Erik P. van den Ban (Universiteit Utrecht): Harmonic analysis of non-Riemannian symmetric spaces
• Tyrone Crisp (University of Maine): Tempered representations from the point of view of Langlands, and from the point of view of operator algebras
• Omar Mohsen (Université de Paris-Saclay): Introduction to hypoelliptic operators and their index theory
• Hang Wang (East China Normal University): Groups C*-algebras and their K-theory