• 2017 Jun 15

# Group actions: Nir Lazarovich (ETH Zurich): Detecting sphere boundaries of hyperbolic groups

10:00am to 11:00am

We show that the boundary of a one-ended simply connected at infinity hyperbolic group with enough codimension-1 surface subgroups is homeomorphic to a sphere. By works of Markovic and Kahn-Markovic our result gives a new characterization of groups which are virtually fundamental groups of hyperbolic 3-manifolds. Joint work with B. Beeker.
• 2017 Jun 01

# Group actions:Lei Yang - badly approximable points on curves and unipotent orbits in homogeneous spaces

10:30am to 11:30am

We will study n-dimensional badly approximable points on curves. Given an analytic non-degenerate curve in R^n, we will show that any countable intersection of the sets of weighted badly approximable points on the curve has full Hausdorff dimension. This strengthens a previous result of Beresnevich by removing the condition on weights. Compared with the work of Beresnevich, we study the problem through homogeneous dynamics. It turns out that the problem is closely related to the study of distribution of long pieces of unipotent orbits in homogeneous spaces.
• 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
• 2017 May 04

# Group actions: Nicolas de Saxcé (Paris 13) - Diophantine approximation and diagonal flows on the space of lattices

10:00am to 11:00am

## Location:

Ross 70
For almost every real number x, the inequality |x-p/q|<1/q^a has finitely many solutions if and only if a>2. By Roth's theorem, any irrational algebraic number x also satisfies this property, so that from that point of view, algebraic numbers and random numbers behave similarly.
• 2017 Apr 27

# Group actions: Yair Glasner (BGU) - On Highly transitive permutation representations of groups.

10:30am to 11:30am

## Location:

Ross 70
Abstract: A permutation representation of a group G is called highly transitive if it is transitive on k-tuples of points for every k. Until just a few years ago groups admitting such permutation representations were thought of as rare. I will focus on three rather recent papers: G-Garion, Hall-Osin, Gelander-G-Meiri (in preparation) showing that such groups are in fact very common.
• 2017 Apr 27

# Group actions: Yair Glasner (BGU) - On Highly transitive permutation representations of groups.

10:30am to 11:30am

## Location:

Ross 70
Abstract: A permutation representation of a group G is called highly transitive if it is transitive on k-tuples of points for every k. Until just a few years ago groups admitting such permutation representations were thought of as rare. I will focus on three rather recent papers: G-Garion, Hall-Osin, Gelander-G-Meiri (in preparation) showing that such groups are in fact very common.
• 2017 Mar 02

# Group actions seminar: David El-Chai Ben Ezra (HUJI) - The congruence subgroup problem for automorphism groups of  free meta-abelian groups

10:30am to 11:30am

• 2017 Mar 02

# Group actions seminar: David El-Chai Ben Ezra (HUJI) - The congruence subgroup problem for automorphism groups of  free meta-abelian groups

10:30am to 11:30am

• 2017 Jan 19

# Groups and dynamics: Manfred Einsiedler (ETH) - Measure Rigidy and Quantitative Recurrence

10:30am to 11:30am

Ross 70
• 2017 Jan 05

# Groups and dynamics: Masaki Tsukamoto (lecture 5)

10:30am to 11:30am

Ross 70