Noncommutative rigidity of higher rank lattices - Part 4 | Vidéo

Noncommutative rigidity of higher rank lattices - Part 4

Apparaît dans la collection : 2024 - T2 - Group actions and rigidity: around the Zimmer program

We survey recent results regarding dynamics of positive definite functions and character rigidity of higher rank lattices. We discuss the notion of noncommutative boundary structure and we give the proof of the noncommutative Nevo–Zimmer structure theorem for ergodic actions of higher rank lattices on von Neumann algebras due to Boutonnet–Houdayer. We present several applications to ergodic theory, topological dynamics, unitary representation theory and operator algebras. We also present a noncommutative analogue of Margulis' factor theorem for higher rank lattices and we explain its relevance towards Connes’ celebrated rigidity conjecture.

Informations sur la vidéo

Date de captation 05/06/2024
Date de publication 05/06/2024
Institut IHP
Langue Anglais
Audience Chercheurs, Doctorants
Réalisateur(s) Alexandre Duplessis, Fabrizio Scapin
Format MP4
Lieu IHP - Darboux Amphitheater

Domaine(s)

Théorie des groupes

Bibliographie

U. Bader, R. Boutonnet, C. Houdayer, J. Peterson, Charmenability of arithmetic groups of product type. Invent. Math. 229 (2022), 929–985.
R. Boutonnet, C. Houdayer, Stationary characters on lattices of semisimple Lie groups. Publ. Math. Inst. Hautes Etudes Sci. 133 (2021), 1–46.
R. Boutonnet, C. Houdayer, The noncommutative factor theorem for lattices in product groups. J. Ec. polytech. Math. 10 (2023), 513–524.