Noncommutative rigidity of higher rank lattices - Part 1 | Vidéo

Noncommutative rigidity of higher rank lattices - Part 1

Appears in 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.

Information about the video

Date of recording 03/06/2024
Date of publication 03/06/2024
Institution IHP
Licence CC BY-NC-ND
Language English
Audience Researchers, Graduate Students
Director(s) Alexandre Duplessis
Format MP4
Venue IHP - Darboux Amphitheater

Domain(s)

Group Theory

Bibliography

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.