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 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 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 Dec 17

    Groups & dynamics: Rene Rühr, Distribution of Shapes of Orthogonal Lattices

    10:00am to 11:30am

    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
  • 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
  • 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
  • 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 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 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

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