# Séminaires : Séminaire de Logique Lyon-Paris

 Equipe(s) : lm, Responsables : S. Anscombe, O. Finkel, A. Khélif, S. Rideau, T. Tsankov, A. Vignati Email des responsables : Salle : Contacter Silvain Rideau ou Alessandro Vignati Adresse : Description

 Orateur(s) Slawomir Solecki - Cornell, Titre Closed subgroups generated by generic measure preserving transformations Date 05/05/2021 Horaire 16:00 à 17:15 Diffusion https://u-paris.zoom.us/rec/share/OyCgdp5b1f_-pDPiNXjXyZ_x4enPhPIxfeFLvo0DDVID1sJY7Wq27oLew0TAJHc.-jCtsYcv5WSBxs1P?startTime=1620223331000 Résume We describe the background and outline a proof of the following theorem: for a generic measure preserving transformation $T$, the closed group generated by $T$ is not isomorphic to the topological group $L^0(\lambda, {\mathbb T})$ of all Lebesgue measurable functions from $[0,1]$ to $\mathbb T$. This result answers a question of Glasner and Weiss. The main step in the proof consists of showing that Koopman representations of ergodic boolean actions of $L^0(\lambda, {\mathbb T})$ possess a non-trivial property not shared by all unitary representations of $L^0(\lambda, {\mathbb T})$. In proving that theorem, an important role is played by a new mean ergodic theorem for ergodic boolean actions of $L^0(\lambda, {\mathbb T})$. Salle Contacter Silvain Rideau ou Alessandro Vignati Adresse