Séminaire de Géométrie, Groupes et Dynamique
# Yair Glasner: "Boomerang subgroups and the Nevo-Stuck-Zimmer theorem"

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Europe/Paris

435 (UMPA)
### 435

#### UMPA

Description

Let be a countable group and its Chabauty space, namely the compact -space of all subgroups of . We call a subgroup a boomerang subgroup if for every , for some subsequence . Poincar\'{e} recurrence implies that -almost every subgroup of is a boomerang, with respect to every invariant random subgroup . I will discuss boomerang subgroups and in particular, I will prove that every boomerang subgroup in is either finite and central or of finite index. This gives a simple new proof for the Nevo-Stuck-Zimmer theorem in this case. More generally this method applies for lattices of the form where is a Chevaley group over .