2016
Dec
08

# Events & Seminars

2016
Dec
29

2016
Mar
03

# Groups & dynamics: Karim Adiprasito (HUJI) - Contractible manifolds, hyperbolicity and the fundamental pro-group at infinity

10:00am to 11:00am

## Location:

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
Nov
17

# Groups and dynamics: Arie Levit

10:30am to 11:30am

## Location:

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
Dec
15

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

10:30am to 11:30am

## Location:

Ross 70

Abstract:

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.

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.

2015
Dec
31

# Groups & dynamics: Thang Neguyen (Weizmann) - Rigidity of quasi-isometric embeddings

10:00am to 11:00am

## Location:

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
Mar
31

# Groups & dynamics: Paul Nelson (ETH) - Quantum variance on quaternion algebras

10:00am to 11:00am

## Location:

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

2015
Dec
02

# Dynamics & probability: Ron Rosenthal (ETHZ) "Local limit theorem for certain ballistic random walks in random environments"

2:00pm to 3:00pm

## Location:

Ross 70

Title: Local limit theorem for certain ballistic random walks in random

environments

Abstract: We study the model of random walks in random environments in

dimension four and higher under Sznitman's ballisticity condition (T').

We prove a version of a local Central Limit Theorem for the model and also

the existence of an equivalent measure which is invariant with respect

to the point of view of the particle. This is a joint work with Noam Berger

and Moran Cohen.

environments

Abstract: We study the model of random walks in random environments in

dimension four and higher under Sznitman's ballisticity condition (T').

We prove a version of a local Central Limit Theorem for the model and also

the existence of an equivalent measure which is invariant with respect

to the point of view of the particle. This is a joint work with Noam Berger

and Moran Cohen.

2015
Nov
10

# Dynamics & probability: Ariel Rapaport (HUJI) " Self-affine measures with equal Hausdorff and Lyapunov dimensions"

2:00pm to 3:00pm

## Location:

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

Title: Self-affine measures with equal Hausdorff and Lyapunov dimensions

Abstract:

Let μ be the stationary measure on ℝd which corresponds to a self-affine iterated function system Φ and a probability vector p. Denote by A⊂Gl(d,ℝ) the linear parts of Φ. Assuming the members of A contract by more than 12, it follows from a result by Jordan, Pollicott and Simon, that if the translations of Φ are drawn according to the Lebesgue measure, then dimHμ=min{D,d} almost surely. Here D is the Lyapunov dimension, which is an explicit constant defined in terms of A and p.

Abstract:

Let μ be the stationary measure on ℝd which corresponds to a self-affine iterated function system Φ and a probability vector p. Denote by A⊂Gl(d,ℝ) the linear parts of Φ. Assuming the members of A contract by more than 12, it follows from a result by Jordan, Pollicott and Simon, that if the translations of Φ are drawn according to the Lebesgue measure, then dimHμ=min{D,d} almost surely. Here D is the Lyapunov dimension, which is an explicit constant defined in terms of A and p.

2015
Dec
15

# Dynamics & probability: Omri Solan (TAU) - Divergent trajectories in SL_3(R)/SL_3(Z)

2:00pm to 4:30pm

## Location:

Manchester building, Hebrew University of Jerusalem, 209

Abstract:

2015
Nov
17

# Dynamics & probability: Sebastian Donoso (HUJI), "Topological structures and the pointwise convergence of some averages for commuting transformations"

2:00pm to 3:00pm

## Location:

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

Title: Topological structures and the pointwise convergence of some averages for commuting transformations

Abstract: ``Topological structures'' associated to a topological dynamical

system are recently developed tools in topological dynamics. They have

several applications, including the characterization of topological

dynamical systems, computing automorphisms groups and even the pointwise

convergence of some averages. In this talk I will discuss some developments

of this subject, emphasizing applications to the pointwise convergence of

Abstract: ``Topological structures'' associated to a topological dynamical

system are recently developed tools in topological dynamics. They have

several applications, including the characterization of topological

dynamical systems, computing automorphisms groups and even the pointwise

convergence of some averages. In this talk I will discuss some developments

of this subject, emphasizing applications to the pointwise convergence of

2015
Nov
24

# Dynamics & probability: Yaar Salomon (Stonybrook) "The Danzer problem and a solution to a related problem of Gowers"

2:00pm to 3:00pm

## Location:

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

The Danzer problem and a solution to a related problem of Gowers

Is there a point set Y in R^d, and C>0, such that every convex

set of volume 1 contains at least one point of Y and at most C? This

discrete geometry problem was posed by Gowers in 2000, and it is a special

case of an open problem posed by Danzer in 1965. I will present two proofs

that answers Gowers' question with a NO. The first approach is dynamical;

we introduce a dynamical system and classify its minimal subsystems. This

Is there a point set Y in R^d, and C>0, such that every convex

set of volume 1 contains at least one point of Y and at most C? This

discrete geometry problem was posed by Gowers in 2000, and it is a special

case of an open problem posed by Danzer in 1965. I will present two proofs

that answers Gowers' question with a NO. The first approach is dynamical;

we introduce a dynamical system and classify its minimal subsystems. This

2015
Nov
02

# Combinatorics seminar

Repeats every week every Monday until Sun Nov 08 2015 .

11:00am to 1:00pmAbstract:

Expander graphs have many wonderful properties, and have been an immensely useful and fruitful area of research in both applicative and theoretical fields. There has been a lot of interest recently in the study of higher dimensional generalizations of expanders to d-uniform hypergraphs. Many competing definitions have been proposed, and different definitions may be appropriate depending on the property of expanders that we wish to preserve.

Expander graphs have many wonderful properties, and have been an immensely useful and fruitful area of research in both applicative and theoretical fields. There has been a lot of interest recently in the study of higher dimensional generalizations of expanders to d-uniform hypergraphs. Many competing definitions have been proposed, and different definitions may be appropriate depending on the property of expanders that we wish to preserve.

2015
Nov
17

# Dynamics lunch: Arie Levit (Weizmann) "Invariant random subgroups"

12:00pm to 1:00pm

## Location:

Manchester building, Hebrew University of Jerusalem, (Coffee Lounge)

Title: Invariant random subgroups

2015
Dec
29

# Dynamics lunch: Tom Gilat (HUJI): "Measure rigidity for `dense' multiplicative semigroups (following Einsiedler and Fish)"

12:00pm to 1:00pm

## Location:

Manchester building, Hebrew University of Jerusalem, (Coffee lounge)