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# Group theory seminar Houdayer/Chawla/Brofferio

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## Group theory seminar Houdayer/Chawla/Brofferio

March 12 (Tuesday)

This seminar meeting will focus on interactions between groups and random walks, and will be dedicated to our beloved mentor and colleague, Anatoly Moiseevich Vershik, who pioneered this field.

14.00 – 14.45 Cyril Houdayer (ENS Paris)  « The noncommutative factor theorem for lattices in product groups ».

15.00 – 15.45   Kunal Chawla (Princeton)   « The Poisson boundary of hyperbolic groups without moment conditions ».

16.15 – 17.00   Sara Brofferio (Université Paris-Est Créteil Val-de-Marne),  « Uniqueness of  invariant measures for random homeomorphisms of the real line ».

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Cyril Houdayer  « The noncommutative factor theorem for lattices in product groups ».

In this talk, I will present a noncommutative analogue of Bader-Shalom factor theorem for lattices with dense projections in product groups. Combining with previous works, this result provides a noncommutative analogue of Margulis factor theorem for all irreducible lattices in higher rank semisimple algebraic groups. Namely, we give a complete description of all intermediate von Neumann subalgebras sitting between the group von Neumann algebra associated with the lattice and the group measure space von Neumann algebra associated with the action of the lattice on the Furstenberg-Poisson boundary. This is joint work with Rémi Boutonnet.

Kunal Chawla,  « The Poisson boundary of hyperbolic groups without moment conditions ».

Sara Brofferio   « Uniqueness of  invariant measures for random homeomorphisms of the real line ».

A stochastic dynamical systems is a Markov process  defined recursively by X_n=\Psi_n(X_{n-1})=\Psi_n\cdots \Psi_1(X_0) where \Psi_n i.i.d. random continuous transformations on a given space M.  X_n can be seen as the process obtained by the action of the  random walk \Psi_n\cdots \Psi_1 on a (semi)-group Gamma acting on some nice metric space M.

In this talk we will focus on stochastic dynamical systems induced  by a random walk on the group of homeomorphisms of R. I will present the results of joint work  with D. Buraczewski and T. Szarek, in which we establish conditions (relatively optimal) that guarantee that the system admits a unique invariant measure (possibly of infinite mass).

- Séminaire de théorie des groupes à l’ENS

#### Détails :

Orateur / Oratrice : Cyril Houdayer, Kunal Chawla, Sara Brofferio
Date : 12 mars 2024
Horaire : 14h00 - 17h00
Lieu : 14:00-17:00 Salle W