Appears in collection : 2025 - T1 - WS2 - Tempered representations and K-theory

Tempered representations of a group are the unitary representations that are weakly contained in the regular representation. The standard way to say that a representation is close to being tempered is probably to use Fell's topology which involves convergence of matrix coefficients. I will discuss another (in general much stronger) notion of closeness, that originates from random matrix theory and the work of Haagerup and Thorbjornsen where is it called strong convergence, and which involves convergence of operator norms. I will present examples, counterexamples, applications, and many questions. Based on joint works with Michael Magee from Durham.