2017
Jun
06

# Eventss

2017
Feb
28

# Dynamics seminar: Emmanuel Roy (Paris 13): Ergodic splittings of Poisson processes

2:00pm to 3:00pm

If N denotes a Poisson process, a splitting of N is formed by two point processes N_1 and N_2 such that N=N_1+N_2.

If N_1 and N_2 are independent Poisson processes then the splitting is said to be Poisson and such a splitting is always available (We allow the possibility to enlarge the ambient probability space).

In general, a splitting is not Poisson but the situation changes if we require that the distributions of the point processes involved are left invariant by a common underlying map that acts at the level of each point of the processes.

If N_1 and N_2 are independent Poisson processes then the splitting is said to be Poisson and such a splitting is always available (We allow the possibility to enlarge the ambient probability space).

In general, a splitting is not Poisson but the situation changes if we require that the distributions of the point processes involved are left invariant by a common underlying map that acts at the level of each point of the processes.

2017
Jun
29

# Special ergodic theory seminar: Abel Farkas (HUJI), Conditional measure on the Brownian path

10:00am to 11:00am

For a given deterministic measure we construct a random measure on the Brownian path that has expectation the given measure. For the construction we introduce the concept of weak convergence of random measures in probability. The machinery can be extended to more general sets than Brownian path.

2017
May
16

# Special dynamics seminar: Ian Morris (Surrey): Equilibrium states of affine iterated function systems

(All day)

## Location:

Equilibrium states of affine iterated function systems

Motivated by the long-standing problem of finding sharp lower estimates for the Hausdorff dimension of self-affine sets, I will describe some recent results on the equilibrium states of the singular value function. These equilibrium states arise as candidates for the measures of maximal Hausdorff dimension on self-affine sets. In particular I will discuss a sufficient condition for uniqueness of the equilibrium state (from joint work with Antti Käenmäki) and an unconditional bound for the number of ergodic equilibrium states (from joint work with Jairo Bochi).

2017
Feb
09

2015
Dec
10

# Groups & dynamics: Shmuel Weinberger (Chicago) - Borel and the symmetry of locally symmetric manifolds. II

10:00am to 11:00am

## Location:

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

# Group actions seminar: Ilya Khayutin (IAS/Princeton) - Joint Equidistribution of CM Points

10:30am to 11:30am

## Location:

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

# Groups & dynamics: Doron Puder (TAU)

10:30am to 11:30am

2015
Dec
03

# Groups & dynamics: Shmuel Weinberger (Chicago) - Borel and the symmetry of locally symmetric manifolds. I

10:00am to 11:20am

## Location:

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

# Group actions/dynamics seminar: Sebastián Donoso (University of O'Higgins, Chile) Quantitative multiple recurrence for two and three transformations

10:00am to 11:00am

## Location:

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

2017
Dec
21

# Groups & Dynamics: Jeremy Kahn (Brown University) - Surface Subgroups in Nonuniform Lattices

10:30am to 11:30am

## Location:

Ross 70

Abstract:

In 2009 the speaker and Vladimir Markovic constructed nearly geodesic surfaces in a given closed hyperbolic 3-manifold M. The construction proceeded by taking all "good pants" in M and matching them at their boundaries to produce a closed surface. I will describe this construction, as well as a new construction with Alexander Wright, of a nearly geodesic surface in the case where M has a cusp. If time permits, I will discuss the potential applications of this construction to higher rank nonuniform lattices and mapping class groups.

In 2009 the speaker and Vladimir Markovic constructed nearly geodesic surfaces in a given closed hyperbolic 3-manifold M. The construction proceeded by taking all "good pants" in M and matching them at their boundaries to produce a closed surface. I will describe this construction, as well as a new construction with Alexander Wright, of a nearly geodesic surface in the case where M has a cusp. If time permits, I will discuss the potential applications of this construction to higher rank nonuniform lattices and mapping class groups.

2017
Oct
31

2017
Nov
07

2017
Nov
28

# Dynamics lunch: Benjy Weiss "Rigidity sequences for weakly mixing transformations"

12:00pm to 1:00pm

Here is a title and abstract for the lunch seminar:

Rigidity sequences for weakly mixing transformations

Abstract: I will present a recent result of Bassam Fayad

and Jean-Paul Thouvenot that shows that any rigidty

sequence for an irrational rotation is also a rigidity

sequence for some weakly mixing transformation.

Rigidity sequences for weakly mixing transformations

Abstract: I will present a recent result of Bassam Fayad

and Jean-Paul Thouvenot that shows that any rigidty

sequence for an irrational rotation is also a rigidity

sequence for some weakly mixing transformation.

2015
Nov
10

# Dynamics lunch: Lei Yang (HUJI) "Proper affine actions and geodesic flows of hyperbolic surfaces"

12:00pm to 1:00pm

## Location:

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

Title: Proper affine actions and geodesic flows of hyperbolic surfaces