Groups & Dynamics

The Groups & Dynamics seminar meets on Thursdays at 10:30 in the Ross building room 70. 
2020 Jan 30

Groups & Dynamics Seminar. Chloe Perin (HUJI): Homogeneity of torsion-free hyperbolic groups

10:00am to 11:00am

Location: 

Ross 70 a
A countable group is said to be homogeneous if whenever tuples of elements u, v satisfy the same first-order formulas there is an automorphism of the group sending one to the other. We had previously proved with Rizos Sklinos that free groups are homogeneous, while most surface groups aren't. In a joint work with Ayala Dente-Byron, we extend this to give a complete characterization of torsion-free hyperbolic groups that are homogeneous.
2020 Jan 23

Groups & Dynamics Seminar. POSTPONED

10:00am to 11:00am

Location: 

Ross 70 a
A countable group is said to be homogeneous if whenever tuples of elements u, v satisfy the same first-order formulas there is an automorphism of the group sending one to the other. We had previously proved with Rizos Sklinos that free groups are homogeneous, while most surface groups aren't. In a joint work with Ayala Dente-Byron, we extend this to give a complete characterization of torsion-free hyperbolic groups that are homogeneous.
2020 Jan 02

Groups & Dynamics Seminar. Maria Gerasimova (BIU) : “Isoperimetry, Littlewood functions, and unitarisability of group”

10:00am to 11:00am

Location: 

Ross 70 a
Let Γ be a discrete group. A group Γ is called unitarisable if for any Hilbert space H and
any uniformly bounded representation π : Γ → B(H) of Γ on H there exists a bounded operator
S : H → H such that S^{−1}π(g)S is a unitary representation for any g ∈ Γ. It is well known that
amenable groups are unitarisable. It has been open ever since whether amenability characterises unitarisability of groups.
Dixmier: Are all unitarisable groups amenable?
One of the approaches to study unitarisability is related to the space of the Littlewood functions
2019 Nov 28

Konstantin Golubev   (ETH) - On non-autocorrelated functions on a hyperbolic surface

10:00am to 11:00am

Location: 

Ross 70
An L^2-function on a finite volume hyperbolic surface is called non-autocorrelated if it is perpendicular to its image under A_r, the operator of averaging over the circle of radius r, where r is fixed. We show that the support of such a function is small, namely, it takes not more than (r+1) / exp(r/2) of the volume of the surface. In my talk, I'll prove this result, and show its connection to the equidistribution of the circle on a surface (proved by Nevo).
2019 Nov 07

Groups & Dynamics seminar: Alex Margolis (Technion) “Almost normal subgroups and quotient spaces״

10:00am to 11:00am

Location: 

Ross 70
Abstract: A subgroup is said to be almost normal if it is commensurable
to all of its conjugates. Even though there may not be a well-defined
quotient group, there is still a well-defined quotient space that admits
an isometric action by the ambient group. We can deduce many geometric
and algebraic properties of the ambient group by examining this action.
In particular, we will use quotient spaces to prove a relative version
of Stallings-Swan theorem on groups of cohomological dimension one. We
2019 Oct 31

Groups & Dynamics seminar - Vincent Guirardel (Universite de Rennes 1) "Measure Equivalence rigidity for Out(Fn)"

10:00am to 11:00am

Location: 

Ross 70
Abstract:
Measure equivalence of countable groups is a measure theoretic analogue
of quasi-isometry.
For example, any two lattices in the same Lie group are by definition
measure equivalent.
We prove that any countable group that is measure equivalent to Out(Fn)
is virtually isomorphic to Out(Fn). This is a joint work with Camille
Horbez.
2019 Jun 27

Groups and Dynamics seminar: Asaf Katz (Chicago) - An application of Margulis' inequality to effective equidistribution.

11:30am to 12:45pm

Abstract: Ratner's celebrated equidistribution theorem states that the trajectory of any point in a homogeneous space under a unipotent flow is getting equidistributed with respect to some algebraic measure. In the case where the action is horospherical, one can deduce an effective equidistribution result by mixing methods, an idea that goes back to Margulis' thesis.

2019 Jun 04

Groups & dynamics seminar: Arie Levit(Yale) - Surface groups are flexibly stable

12:00pm to 1:00pm

Abstract: 
A group G is stable in permutations if every almost-action of G on a finite set is close to some actual action. Part of the interest in this notion comes from the observation that a non-residually finite stable group cannot be sofic. 
I will show that surface groups are stable in a flexible sense, that is if one is allowed to "add a few extra points" to the action. This is the first non-trivial stability result for a non-amenable group. 
2019 May 21

Special groups theory seminar: Abdalrazzaq R A Zalloum (Suny Buffalo) "Regular languages for hyperbolic-like geodesics".

4:00pm to 5:00pm

Location: 

Ross 63
Combinatorial group theory began with Dehn's study of surface groups, where he used arguments from hyperbolic geometry to solve the word/conjugacy problems. In 1984, Cannon generalized those ideas to all "hyperbolic groups", where he was able to give a solution to the word/conjugacy problem, and to show that their growth function satisfies a finite linear recursion. The key observation that led to his discoveries is that the global geometry of a hyperbolic group is determined locally: first, one discovers the local picture of G, then the recursive structure

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