Groups & Dynamics

  • 2016 Dec 15

    Groups and dynamics: Yair Hartman (Northwestern) - Percolation, Invariant Random Subgroups and Furstenberg Entropy

    10:30am to 11:30am

    Location: 

    Ross 70
    Abstract:
    In this talk I'll present a joint work with Ariel Yadin, in which we solve the Furstenberg Entropy Realization Problem for finitely supported random walks (finite range jumps) on free groups and lamplighter groups. This generalizes a previous result of Bowen. The proof consists of several reductions which have geometric and probabilistic flavors of independent interests.
    All notions will be explained in the talk, no prior knowledge of Invariant Random Subgroups or Furstenberg Entropy is assumed.
  • 2016 Nov 24

    Groups and dynamics- Oren Becker

    10:30am to 11:30am

    Location: 

    Ross 70
    Speaker: Oren Becker
    Title: Locally testable groups
    Abstract:
    Arzhantseva and Paunescu [AP2015] showed that if two permutations X and Y in Sym(n) nearly commute (i.e. XY is close to YX), then the pair (X,Y) is close to a pair of permutations that really commute.
  • 2016 Nov 17

    Groups and dynamics: Arie Levit

    10:30am to 11:30am

    Location: 

    Ross 70
    Speaker: Arie Levit
    Weizmann Institute
    Title: Local rigidity of uniform lattices
    Abstract: A lattice is topologically locally rigid (t.l.r) if small deformations of it are isomorphic lattices. Uniform lattices in Lie groups were shown to be t.l.r by Weil [60']. We show that uniform lattices are t.l.r in any compactly generated topological group.
  • 2016 Nov 03

    Monodromy groups & Arithmetics groups

    Lecturer: 

    V.N. Venkataramana
    2:30pm

    Location: 

    Lecture Hall 2
    To a linear differential equation on the projective line with finitely many points of singularities, is associated a monodromy group; when the singularities are "reguar singular", then the monodromy group gives more or less complete information about the (asymptotics of the ) solutions. 

    The cases of interest are the hypergeometric differential equations, and there is much recent work in this area, centred around a question of Peter Sarnak on the arithmeticity/thin-ness of these monodromy groups. I give a survey of these recent results.
  • 2016 Nov 03

    Groups and dynamics - Misha Belolipetsky

    10:30am to 11:30am

    Location: 

    Ross 70
    Speaker: Misha Belolipetsky
    Title: Arithmetic Kleinian groups generated by elements of finite order
    Abstract:
    We show that up to commensurability there are only finitely many
    cocompact arithmetic Kleinian groups generated by rotations. The proof
    is based on a generalised Gromov-Guth inequality and bounds for the
    hyperbolic and tube volumes of the quotient orbifolds. To estimate the
    hyperbolic volume we take advantage of known results towards Lehmer's
    problem. The tube volume estimate requires study of triangulations of
  • 2016 Nov 03

    Groups and dynamics - Misha Belolipetsky

    10:30am to 11:30am

    Location: 

    Ross 70
    Arithmetic Kleinian groups generated by elements of finite order Abstract: We show that up to commensurability there are only finitely many cocompact arithmetic Kleinian groups generated by rotations. The proof is based on a generalised Gromov-Guth inequality and bounds for the hyperbolic and tube volumes of the quotient orbifolds. To estimate the hyperbolic volume we take advantage of known results towards Lehmer's problem. The tube volume estimate requires study of triangulations of lens spaces which may be of independent interest.

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