2016
Dec
01

# Groups and dynamics: Masaki Tsukamoto (lecture 1)

10:30am to 11:30am

## Location:

Ross 70

INTRODUCTION TO MEAN DIMENSION AND THE EMBEDDING PROBLEM OF DYNAMICAL SYSTEMS (Part 1)

2016
Dec
01

10:30am to 11:30am

Ross 70

INTRODUCTION TO MEAN DIMENSION AND THE EMBEDDING PROBLEM OF DYNAMICAL SYSTEMS (Part 1)

2016
Nov
17

10:30am to 11:30am

Ross 70

Speaker: 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.

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
Mar
03

10:00am to 11:00am

Ross building, Hebrew University of Jerusalem, (Room 70)

To every topological group, one can associate a unique universal

minimal flow (UMF): a flow that maps onto every minimal flow of the

group. For some groups (for example, the locally compact ones), this

flow is not metrizable and does not admit a concrete description.

However, for many "large" Polish groups, the UMF is metrizable, can be

computed, and carries interesting combinatorial information. The talk

will concentrate on some new results that give a characterization of

metrizable UMFs of Polish groups. It is based on two papers, one joint

minimal flow (UMF): a flow that maps onto every minimal flow of the

group. For some groups (for example, the locally compact ones), this

flow is not metrizable and does not admit a concrete description.

However, for many "large" Polish groups, the UMF is metrizable, can be

computed, and carries interesting combinatorial information. The talk

will concentrate on some new results that give a characterization of

metrizable UMFs of Polish groups. It is based on two papers, one joint

2016
Dec
22

2015
Dec
31

10:00am to 11:00am

Ross building, Hebrew University of Jerusalem, (Room 70)

To every topological group, one can associate a unique universal

minimal flow (UMF): a flow that maps onto every minimal flow of the

group. For some groups (for example, the locally compact ones), this

flow is not metrizable and does not admit a concrete description.

However, for many "large" Polish groups, the UMF is metrizable, can be

computed, and carries interesting combinatorial information. The talk

will concentrate on some new results that give a characterization of

metrizable UMFs of Polish groups. It is based on two papers, one joint

minimal flow (UMF): a flow that maps onto every minimal flow of the

group. For some groups (for example, the locally compact ones), this

flow is not metrizable and does not admit a concrete description.

However, for many "large" Polish groups, the UMF is metrizable, can be

computed, and carries interesting combinatorial information. The talk

will concentrate on some new results that give a characterization of

metrizable UMFs of Polish groups. It is based on two papers, one joint

2016
Dec
08

2015
Nov
12

10:00am to 11:00am

Ross 70

Title: Rigidity of higher rank diagonalizable actions in positive characteristic

2015
Nov
19

10:00am to 11:00am

Ross 70

Title: Equidistribution of expanding translates of curves in homogeneous spaces and Diophantine approximation.
Abstract:
We consider an analytic curve $\varphi: I \rightarrow \mathbb{M}(n\times m, \mathbb{R}) \hookrightarrow \mathrm{SL}(n+m, \mathbb{R})$ and embed it into some homogeneous space $G/\Gamma$, and translate it via some diagonal flow

2015
Nov
05

9:45am to 11:00am

Manchester building, Hebrew University of Jerusalem, (Room 209)

Title: Arithmetic of Double Torus Quotients and the Distribution of Periodic Torus Orbits
Abstract:
In this talk I will describe some new arithmetic invariants for pairs of torus orbits on inner forms of PGLn and SLn. These invariants allow us to significantly strengthen results towards the equidistribution of packets of periodic torus orbits on higher rank S-arithmetic quotients. An important aspect of our method is that it applies to packets of periodic orbits of maximal tori which are only partially split.

2015
Dec
17

12:00pm to 1:00pm

Einstein 110

Consider a sequence of random walks on $\mathbb{Z}/p\mathbb{Z}$ with symmetric generating sets $A= A(p)$. I will describe known and new results regarding the mixing time and cut-off. For instance, if the sequence $|A(p)|$ is bounded then the cut-off phenomenon does not occur, and more precisely I give a lower bound on the size of the cut-off window in terms of $|A(p)|$. A natural conjecture from random walk on a graph is that the total variation mixing time is bounded by maximum degree times diameter squared.

2015
Dec
10

10:00am to 11:00am

Ross building, Hebrew University of Jerusalem, (Room 70)

Abstract

Borel studied the topological group actions that are

possible on locally symmetric manifolds. In these two talks, I will

explain Borel's work and interpret these results as a type of rigidity

statement very much related to the well-known Borel conjecture of high

dimensional topology. In particular, I will give the characterization

of locally symmetric manifolds (of dimension not 4) which have a

unique maximal conjugacy of finite group of orientation preserving

homeomorphisms, due to Cappell, Lubotzky and myself. We will then

Borel studied the topological group actions that are

possible on locally symmetric manifolds. In these two talks, I will

explain Borel's work and interpret these results as a type of rigidity

statement very much related to the well-known Borel conjecture of high

dimensional topology. In particular, I will give the characterization

of locally symmetric manifolds (of dimension not 4) which have a

unique maximal conjugacy of finite group of orientation preserving

homeomorphisms, due to Cappell, Lubotzky and myself. We will then

2018
Jan
04

10:30am to 11:30am

Ross 70

A sequence of Picard/Galois orbits of special points in a product of arbitrary many modular curves is conjectured to equidistribute in the product space as long as it escapes any closed orbit of an intermediate subgroup. This conjecture encompasses several well-known results and conjectures, including Duke's Theorem, the Michel-Venkatesh mixing conjecture and the equidistribution strengthening of André-Oort in this setting.

2017
Dec
07

10:30am to 11:30am

2015
Dec
03

10:00am to 11:20am

Ross building, Hebrew University of Jerusalem, (Room 70)

Abstract:

Borel studied the topological group actions that are

possible on locally symmetric manifolds. In these two talks, I will

explain Borel's work and interpret these results as a type of rigidity

statement very much related to the well-known Borel conjecture of high

dimensional topology. In particular, I will give the characterization

of locally symmetric manifolds (of dimension not 4) which have a

unique maximal conjugacy of finite group of orientation preserving

homeomorphisms, due to Cappell, Lubotzky and myself. We will then

Borel studied the topological group actions that are

possible on locally symmetric manifolds. In these two talks, I will

explain Borel's work and interpret these results as a type of rigidity

statement very much related to the well-known Borel conjecture of high

dimensional topology. In particular, I will give the characterization

of locally symmetric manifolds (of dimension not 4) which have a

unique maximal conjugacy of finite group of orientation preserving

homeomorphisms, due to Cappell, Lubotzky and myself. We will then

2017
May
25

10:00am to 11:00am

Ross 70

In this talk I will provide some counter-examples for quantitative multiple

recurrence problems for systems with more than one transformation. For

instance, I will show that there exists an ergodic system

$(X,\mathcal{X},\mu,T_1,T_2)$ with two commuting transformations such that

for every $\ell < 4$ there exists $A\in \mathcal{X}$ such that

\[ \mu(A\cap T_1^n A\cap T_2^n A) < \mu(A)^{\ell} \]

for every $n \in \mathbb{N}$.

The construction of such a system is based on the study of ``big'' subsets

recurrence problems for systems with more than one transformation. For

instance, I will show that there exists an ergodic system

$(X,\mathcal{X},\mu,T_1,T_2)$ with two commuting transformations such that

for every $\ell < 4$ there exists $A\in \mathcal{X}$ such that

\[ \mu(A\cap T_1^n A\cap T_2^n A) < \mu(A)^{\ell} \]

for every $n \in \mathbb{N}$.

The construction of such a system is based on the study of ``big'' subsets