# Séminaires : Séminaire Général de Logique

 Equipe(s) : lm, Responsables : S. Anscombe, A. Khélif, A. Vignati Email des responsables : sylvy.anscombe@imj-prg.fr, vignati@imj-prg.fr Salle : 1013 Adresse : Sophie Germain Description

 Orateur(s) Anush Tserunyan - McGill University, Titre Backward and forward ergodic theorems along trees Date 26/05/2021 Horaire 16:00 à 17:15 Diffusion https://u-paris.zoom.us/rec/share/f3Rkljh1DzXbDUllrye21BnK5OMUWSWrH4kkGGvRkGS6V8oerMJYfl586Eipq96F.LB4Eyvr8uHR1Yqhi Résume In the classical pointwise ergodic theorem for a probability measure preserving (pmp) transformation $T$, one takes averages of a given integrable function over the intervals $\{x, T(x), T^2(x), \hdots, T^n(x)\}$ in the forward orbit of the point $x$. In joint work with Jenna Zomback, we prove a “backward” ergodic theorem for a countable-to-one pmp $T$, where the averages are taken over arbitrary subtrees of the graph of $T$ that are rooted at $x$ and lie behind $x$ (in the direction of $T^{-1}$). Somewhat surprisingly, this theorem yields (forward) ergodic theorems for countable groups, in particular, one for pmp actions of free groups of finite rank where the averages are taken along arbitrary subtrees of the standard Cayley graph rooted at the identity. This strengthens results of Grigorchuk (1987), Nevo (1994), and Bufetov (2000). Salle 1013 Adresse Sophie Germain