Groups & Dynamics

  • 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.
  • 2017 Nov 02

    Group actions: Remi Coulon (Rennes) - Growth gap in hyperbolic groups and amenability

    10:30am to 11:30am

    Location: 

    hyperbolic groups and amenability
    (joint work with Françoise Dal'Bo and Andrea Sambusetti)
    Given a finitely generated group G acting properly on a metric space X,
    the exponential growth rate of G with respect to X measures "how big"
    the orbits of G are. If H is a subgroup of G, its exponential growth
    rate is bounded above by the one of G. In this work we are interested in
    the following question: what can we say if H and G have the same
    exponential growth rate? This problem has both a combinatorial and a
    geometric origin. For the combinatorial part, Grigorchuck and Cohen
  • 2017 Nov 02

    Group actions: Remi Coulon (Rennes) - Growth gap in hyperbolic groups and amenability

    10:30am to 11:30am

    Location: 

    hyperbolic groups and amenability
    (joint work with Françoise Dal'Bo and Andrea Sambusetti) Given a finitely generated group G acting properly on a metric space X, the exponential growth rate of G with respect to X measures "how big" the orbits of G are. If H is a subgroup of G, its exponential growth rate is bounded above by the one of G. In this work we are interested in the following question: what can we say if H and G have the same exponential growth rate? This problem has both a combinatorial and a geometric origin.
  • 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 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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