##### Department of Mathematics,

University of California San Diego

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### Department Colloquium

## Prof. Cyril Houdayer

#### Université Paris-Saclay

## Noncommutative ergodic theory of higher rank lattices

##### Abstract:

I will survey recent results regarding the dynamics of positive definite functions and character rigidity of irreducible lattices in higher-rank semisimple algebraic groups. These results have several applications to ergodic theory, topological dynamics, unitary representation theory, and operator algebras. In the case of lattices in higher-rank simple algebraic groups, I will explain the key operator algebraic novelty, which is a noncommutative Nevo-Zimmer theorem for actions on von Neumann algebras. I will also present a noncommutative Margulis' factor theorem and discuss its relevance regarding Connes' rigidity conjecture for group von Neumann algebras of higher-rank lattices.

Host: Adrian Ioana

### March 23, 2023

### 4:00 PM

APM 6402

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