# Séminaires : Séminaire Général de Logique

 Equipe(s) : lm, Responsables : S. Anscombe, A. Khélif, A. Vignati Email des responsables : sylvy.anscombe@imj-prg.fr, vignati@imj-prg.fr Salle : 1013 Adresse : Sophie Germain Description

 Orateur(s) Yury Neretin - University of Vienna, Titre On closures of groups in unitary representations Date 26/09/2022 Horaire 15:15 à 16:15 Diffusion Résume Consider a topological group  $G$ and its unitary representation $\rho$. Consider the closure of $\rho(G)$ in the weak operator topology. Then we get a compact semigroup with separately continuous multiplication. For semisimple Lie groups with finite center this semigroup is simply the one-point compactification (R.Howe  and C.Moore). However, for Abelian  groups (for instance for $\mathbb Z$) and for infinite-dimensional groups this leads to highely nontrivial (but handable) objects. The purpose of talk is an introduction to problems of this type (we do not suppose any preliminary knowledge of representation theory). Salle 1013 Adresse Sophie Germain