Séminaire Géométrie et groupes discrets
# Confined Subgroups of Semisimple Lie Groups

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Europe/Paris

Amphithéâtre Léon Motchane (IHES)
### Amphithéâtre Léon Motchane

#### IHES

Le Bois Marie
35, route de Chartres
91440 Bures-sur-Yvette

Description

Let G be a semisimple Lie group, e.g. G = SL(n,R). A subgroup Γ of G is called *confined* if there is a bounded neighborhood of the identity that contains a non-trivial element of every conjugate of Γ. For example, any normal subgroup of a co-compact lattice is confined. In joint work with Tsachik Gelander, we proved that when G has higher rank (e.g. G = SL(n,R) with n>2), a discrete subgroup of G is confined if and only if it is a lattice, which can be seen as an extension of Margulis' Normal Subgroup Theorem. The proof consists of two independent steps that I hope to explain in my talk: 1) the passage from discrete subgroups to stationary random subgroups and 2) the classification of discrete stationary random subgroups in higher rank. If time permits, I will also discuss some open questions related to this work.

Organized by

Fanny Kassel

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