Groups & Dynamics

2015 Dec 17

Groups & dynamics: Robert Hough (IAS) - Mixing and cut-off on cyclic groups

12:00pm to 1:00pm

Location: 

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 Nov 19

Groups & dynamics: Lei Yang (HUJI) "Equidistribution of expanding translates of curves in homogeneous spaces and Diophantine approximation"

10:00am to 11:00am

Location: 

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

Groups & Dynamics : Ilya Khayutin (HUJI)

9:45am to 11:00am

Location: 

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.
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.
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
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.
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
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 of $\mathbb{N}^2$ and $\mathbb{N}^3$  satisfying combinatorial properties.  
2015 Dec 17

Groups & dynamics: Robert Hough (IAS) - Mixing and cut-off on cyclic groups

12:00pm to 1:00pm

Location: 

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 Nov 19

Groups & dynamics: Lei Yang (HUJI) "Equidistribution of expanding translates of curves in homogeneous spaces and Diophantine approximation"

10:00am to 11:00am

Location: 

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
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. 

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