# Séminaires : Séminaire d'Algèbres d'Opérateurs

 Equipe(s) : ao, Responsables : Pierre Fima, François Le Maître, Romain Tessera Email des responsables : Salle : 1013 Adresse : Sophie Germain Description

 Orateur(s) Anush Tserunyan - , Titre Hyperfinite subequivalence relations of treed equivalence relations Date 04/06/2020 Horaire 16:00 à 17:00 Diffusion Résume A large part of measured group theory studies structural properties of countable groups that hold "on average". This is made precise by studying the orbit equivalence relations induced by free Borel actions of these groups on a standard probability space. In this vein, the amenable groups correspond to hyperfinite equivalence relations, and the free groups to the treeable ones. In joint work with R. Tucker-Drob, we give a detailed analysis of the structure of hyperfinite subequivalence relations of a treed equivalence relation on a standard probability space, deriving the analogues of structural properties of amenable subgroups (copies of $\mathbb{Z}$) of a free group. Most importantly, just like every such subgroup is contained in a unique maximal one, we show that even in the non-pmp setting, every hyperfinite subequivalence relation is contained in a unique maximal one. Salle 1013 Adresse Sophie Germain