BGU Probability and Ergodic Theory (PET) seminar Ical Atom

A weekly seminar featuring a variety of research of talks in or related to Probability theory and dynamics, interpreted in a broad sense (ergodic theory, topological dynamics, group actions…) The seminar runs on Thursdays at 11:10 am in room -101.

The seminar meets on Thursdays, 11:10-12:00, in -101

This Week

Yair Glasner (BGU)

Rigid actions of hyperbolic groups admit only commutative factors

(joint work with Tattwamasi Amrutam and Eli Glasner) Let (X,\Gamma) be a minimal equicontinuous (or more generally rigid) topological dynamical system, with a discrete countable acting group. Intermediate C^-algebras of the form C^_r(\Gamma) < \mathcal{A} < C(X) \rtimes \Gamma, can be thought of as non-commutative generalizations of \Gamma-factors X \rightarrow Y as each such factor gives rise to an intermediate algebra of the form \mathcal{A} = C(Y) \rtimes \Gamma. When the group \Gamma is Gromov hyperbolic we show that this is the only possible source of intermediate algebras. The proof relies on a delicate interplay betwee two actions: The given dynamical system (X,\Gamma) and the boundary action (Z,\Gamma).

2025–26–A meetings

Upcoming Meetings

Date
Title
Speaker
Abstract
Nov 13 Rigid actions of hyperbolic groups admit only commutative factors Yair Glasner (BGU)

(joint work with Tattwamasi Amrutam and Eli Glasner) Let (X,\Gamma) be a minimal equicontinuous (or more generally rigid) topological dynamical system, with a discrete countable acting group. Intermediate C^-algebras of the form C^_r(\Gamma) < \mathcal{A} < C(X) \rtimes \Gamma, can be thought of as non-commutative generalizations of \Gamma-factors X \rightarrow Y as each such factor gives rise to an intermediate algebra of the form \mathcal{A} = C(Y) \rtimes \Gamma. When the group \Gamma is Gromov hyperbolic we show that this is the only possible source of intermediate algebras. The proof relies on a delicate interplay betwee two actions: The given dynamical system (X,\Gamma) and the boundary action (Z,\Gamma).
Nov 20 TBA Michael Glasner (Weizmann Institute)

TBA
Nov 27 TBA Eitan Sapir (BGU)

TBA
Dec 11 TBA Robert Simon (London School of Economics and Political Sciences)
Dec 18 TBA Daniel Tsodikovich

Past Meetings

Date
Title
Speaker
Abstract
Oct 30 Retraction theorems in group-compactifications. Tomer Zimhoni (BGU)

Let $\Gamma$ be a discrete countable infinite Group and let $X$ be compact minimal $\Gamma$-space. A $\Gamma$-compactification by $X$ is a compact topology on $\Gamma\cup X$ on which $\Gamma$ acts continuously by left multiplication and the original action on $X$ respectively, and such that $\Gamma$ is dense in $\Gamma\cup X$.

Is there more than one way to “glue” $X$ to $\Gamma$ in such a way? Are there canonical families of $\Gamma$ compactifications? and what all of this has to do with the old and famous Brouwer’s non-retract theorem from classical topology?

Based on a joint work with Yair Hartman, Aranka Hrušková & Mehrdad Kalantar
Nov 6 Small ball estimates and mixing for word maps on unitary groups Itay Glazer (Technion)

Let w(x,y) be a word in a free group. For any group G, w induces a word map w:G^2–>G. For example, the commutator word w=xyx^(-1)y^(-1) induces the commutator map. In the setting of finite simple groups, Larsen, Shalev and Tiep showed there exists epsilon(w)>0 (depending only on the word w), such that for all sufficiently large G, the probability that a random pair (g_1,g_2) in G^2 satisfies w(g_1,g_2)=g is smaller than |G|^(-epsilon(w)). They further obtained uniform upper bounds on the L^1- and L^infty-mixing times for the random walks induced by the corresponding word measures.
I will discuss analogous results for the family of unitary groups in all ranks.

Seminar run by Tomer Zimhoni, Mr. Liran Ron and Prof. Tom Meyerovitch