This page list all events and seminars that take place in the department this week. Please use the form below to choose a different week or date range.

Colloquium

Symplectic maps: algebra, geometry, dynamics

Mar 22, 14:30—15:30, 2022, Math -101

Speaker

Leonid Polterovich (Tel Aviv University)

Abstract

Symplectic maps can be considered as symmetries of a geometric structure (a symplectic form) on a manifold, and as a mathematical model of admissible motions of classical mechanics. I discuss a number of rigidity phenomena of algebraic, geometric, and dynamical nature exhibited by these maps, focusing on a recent work with Egor Shelukhin.

BGU Probability and Ergodic Theory (PET) seminar

Entropy, ultralimits and Poisson boundaries Online

Mar 24, 11:10—12:00, 2022, -101

Speaker

Elad Sayag (Tel-Aviv University)

Abstract

In many important actions of groups there are no invariant measures. For example: the action of a free group on its boundary and the action of any discrete infinite group on itself. The problem we will discuss in this talk is ‘On a given action, how invariant measure can be?’. Our measuring of non-invariance will be based on entropy (f-divergence). In the talk I will describe the solution of this problem for the free group acting on its boundary and on itself. For doing so we will introduce the notion of ultra-limit of G-spaces, and give a new description of the Poisson-Furstenberg boundary of (G,k) as an ultra-limit of G action on itself, with ‘Abel sum’ measures. Another application will be that amenable groups possess KL-almost-invariant measures (KL stands for the Kullback-Leibler divergence).

All relevant notions, including the notion of Poisson-Furstenberg boundary and the notion of ultra-filters will be explained during the talk.

This is a master thesis work under the supervision of Yehuda Shalom.


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