2016
Dec
29

# Groups & Dynamics

- 2016 Dec 22
- 2016 Dec 15
# Groups and dynamics: Yair Hartman (Northwestern) - Percolation, Invariant Random Subgroups and Furstenberg Entropy

10:30am to 11:30am## Location:

Ross 70Abstract:

In this talk I'll present a joint work with Ariel Yadin, in which we solve the Furstenberg Entropy Realization Problem for finitely supported random walks (finite range jumps) on free groups and lamplighter groups. This generalizes a previous result of Bowen. The proof consists of several reductions which have geometric and probabilistic flavors of independent interests.

All notions will be explained in the talk, no prior knowledge of Invariant Random Subgroups or Furstenberg Entropy is assumed. - 2016 Dec 08
- 2016 Dec 01
# Groups and dynamics: Masaki Tsukamoto (lecture 1)

10:30am to 11:30am## Location:

Ross 70INTRODUCTION TO MEAN DIMENSION AND THE EMBEDDING PROBLEM OF DYNAMICAL SYSTEMS (Part 1) - 2016 Nov 24
# Groups and dynamics- Oren Becker

10:30am to 11:30am## Location:

Ross 70Speaker: Oren Becker

Title: Locally testable groups

Abstract:

Arzhantseva and Paunescu [AP2015] showed that if two permutations X and Y in Sym(n) nearly commute (i.e. XY is close to YX), then the pair (X,Y) is close to a pair of permutations that really commute. - 2016 Nov 17
# Groups and dynamics: Arie Levit

10:30am to 11:30am## Location:

Ross 70Speaker: Arie Levit

Weizmann Institute

Title: Local rigidity of uniform lattices

Abstract: A lattice is topologically locally rigid (t.l.r) if small deformations of it are isomorphic lattices. Uniform lattices in Lie groups were shown to be t.l.r by Weil [60']. We show that uniform lattices are t.l.r in any compactly generated topological group. - 2016 Nov 03
# Monodromy groups & Arithmetics groups

## Lecturer:

V.N. Venkataramana2:30pm## Location:

Lecture Hall 2To a linear differential equation on the projective line with finitely many points of singularities, is associated a monodromy group; when the singularities are "reguar singular", then the monodromy group gives more or less complete information about the (asymptotics of the ) solutions.

The cases of interest are the hypergeometric differential equations, and there is much recent work in this area, centred around a question of Peter Sarnak on the arithmeticity/thin-ness of these monodromy groups. I give a survey of these recent results. - 2016 Nov 03
# Groups and dynamics - Misha Belolipetsky

10:30am to 11:30am## Location:

Ross 70Speaker: Misha Belolipetsky

Title: Arithmetic Kleinian groups generated by elements of finite order

Abstract:

We show that up to commensurability there are only finitely many

cocompact arithmetic Kleinian groups generated by rotations. The proof

is based on a generalised Gromov-Guth inequality and bounds for the

hyperbolic and tube volumes of the quotient orbifolds. To estimate the

hyperbolic volume we take advantage of known results towards Lehmer's

problem. The tube volume estimate requires study of triangulations of - 2016 Nov 03
# Groups and dynamics - Misha Belolipetsky

10:30am to 11:30am## Location:

Ross 70Arithmetic Kleinian groups generated by elements of finite order Abstract: We show that up to commensurability there are only finitely many cocompact arithmetic Kleinian groups generated by rotations. The proof is based on a generalised Gromov-Guth inequality and bounds for the hyperbolic and tube volumes of the quotient orbifolds. To estimate the hyperbolic volume we take advantage of known results towards Lehmer's problem. The tube volume estimate requires study of triangulations of lens spaces which may be of independent interest.