Noncommutative rigidity of higher rank lattices - Part 2
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.
