# Groups & Dynamics

The Groups & Dynamics seminar meets on Thursdays at 10:30 in the Ross building room 70.
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 16

5:00pm to 6:00pm

2019 Jun 12

1:20pm to 2:20pm

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
2019 Jun 27

# Group and dynamics seminar: Michael Chapman (HUJI): Cutoff on Ramanujan complexes

10:00am to 11:15am

Ross 70
2019 Apr 11

# Groups & Dynamics Seminar: Erez Nesharim (Technion) - The t-adic Littlewood conjecture is false

10:00am to 11:00am

## Location:

Ross 70
The Littlewood and the p-adic Littlewood conjectures are famous open problems on the border between number theory and dynamics. In a joint work with Faustin Adiceam and Fred Lunnon we show that the analogue of the p-adic Littlewood conjecture over \mathbb{F}_3((1/t)) is false. The counterexample is given by the Laurent series whose coefficients are the regular paper folding sequence, and the method of proof is by reduction to the non vanishing of certain Hankel determinants.
2019 May 02

# Kobi Peterzil (Haifa) - Closure of o-minimal flows on nilmanifolds

10:00am to 11:00am

I will discuss joint work with S. Starchenko, which combines dynamical systems in the nilmanifold setting with definable objects in o-minimal structures (e.g. semi-algebraic sets): Let G be a real algebraic unipotent group and let L be a lattice in G with p:G->G/L the quotient map. Given a subset X of G which is semi-algerbaic, or more generally definable in an o-minimal structure, we describe the closure of p(X) in terms of finitely many definable families of cosets of positive dimensional algebraic subgroups of G.
2019 Mar 14

# Manuel Luethi (ETH) : Effective equidistribution of primitive rational points along long horocycle orbits and disjointness to Kloosterman sums

10:00am to 11:30am

## Location:

Ross 70
Abstract: An observation by Jens Marklof shows that the primitive rational points of a fixed denominator along the periodic unipotent orbit of volume equal to the square of the denominator equidistribute inside a proper submanifold of the modular surface. This concentration as well as the equidistribution are intimately related to classical questions of number theoretic origin. We discuss the distribution of the primitive rational points along periodic orbits of intermediate size. In this case, we can show joint equidistribution with polynomial rate in the modular surface and in the torus.
2019 Feb 07

# Special group actions seminar. On Tame Subgroups of Finitely Presented Groups: Prof. Rita Gitik, University of Michigan, Ann Arbor.

10:00am to 11:00am

## Location:

Ross 70
We describe several examples of tame subgroups of finitely presented groups and prove that the fundamental groups of certain finite graphs of groups are locally tame.
2018 May 31

# Groups & Dynamics: Anish Gosh (TIFR) - The metric theory of dense lattice orbits

10:30am to 11:30am

Abstract: The classical theory of metric Diophantine approximation is very well developed and has, in recent years, seen significant advances, partly due to connections with homogeneous dynamics. Several problems in this subject can be viewed as particular examples of a very general setup, that of lattice actions on homogeneous varieties of semisimple groups. The latter setup presents significant challenges, including but not limited to, the non-abelian nature of the objects under study.
2018 Jun 14

# Groups & Dynamics seminar. Mark Sapir (Vanderbilt): S-machines and their applications

10:30am to 12:00pm

## Location:

Ross 70
Title: S-machines and their applications Abstract: I will discuss applications of S-machines which were first introduced in 1996. The applications include * Description of possible Dehn functions of groups * Various Higman-like embedding theorems * Finitely presented non-amenable torsion-by-cyclic groups * Aspherical manifolds containing expanders * Groups with quadratic Dehn functions and undecidable conjugacy problem