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Alexander Lubotzky

  1. Sieve methods in group theory II: The Mapping Class Group.

    Чт, 04/14/2011 - 15:01 — SomNambul
    Authors: Alexander Lubotzky, Chen Meiri
    Subjects: Group Theory
    Abstract

    We prove that the set of pseudo-Anosov elements in the Torelli group is
    exponentially small.

  2. Lattices with and lattices without spectral gap.

    Втр, 09/08/2009 - 12:16 — SomNambul
    Authors: Bachir Bekka, Alexander Lubotzky
    Subjects: Dynamical Systems
    Abstract

    The following two results are shown.

    1) Let $G$ be the $k$-rational points of a simple algebraic group over a
    local field $k$ and let $H$ be a lattice in $G.$ Then the regular
    representation of $G$ on $L^2(G/H)$ has a spectral gap (that is, there are
    almost invariant unit vectors in the subspace of functions in $L^2(G/H)$ with
    zero mean).

  3. Lattices with and lattices without spectral gap.

    Втр, 09/08/2009 - 12:16 — SomNambul
    Authors: Bachir Bekka, Alexander Lubotzky
    Subjects: Dynamical Systems
    Abstract

    The following two results are shown.

    1) Let $G$ be the $k$-rational points of a simple algebraic group over a
    local field $k$ and let $H$ be a lattice in $G.$ Then the regular
    representation of $G$ on $L^2(G/H)$ has a spectral gap (that is, there are
    almost invariant unit vectors in the subspace of functions in $L^2(G/H)$ with
    zero mean).

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