Second meeting, Tel Aviv University, 10.1.16, Schreiber building

  • 9:30 cookies, small pastries and fruit

  • 10:00 Yehuda Shalom, TAU

    Schreiber room 8

    Uniform exponential escape of random matrix products from algebraic subgroups and a generalization of Leighton's combinatorial common covering theorem.

    We shall discuss a general non-concentration result for random matrix products, which is a key ingredient in the vast literature on super-strong approximation following the famous work of Bourgain-Gamburd. While this has always been a very technical step, our entirely different approach is much softer, and covers also, for the first time, the case of positive characteristics. A special role in the proof is played by a spectral extension of a famous theorem of Leighton: if two finite graphs admit the same universal covering (tree), then they admit a finite common covering. A Riemannian version of this result is discussed as well.

    Joint work with Asaf Hadari.

  • 11:15 Izhar Oppenheim, BGU

    Schreiber room 8

    A strengthened version of Banach property (T) and angles between projections

    This lecture has two aims: first, to introduce a new definition of a strengthened version of Banach property (T) inspired by V. Lafforgue’s work on strong Banach property (T). Second, to present a criterion for this version of Banach property (T) based on the idea of angles between projections.

  • 12:15 Lunch and informal discussions

  • 13:45 Ferran Valdez, UNAM Morelia, Mexico

    Schreiber room 8

    Affine symmetries of translation surfaces

    In this talk we will discuss what we know about affine symmetries of translation surfaces. We will put special interest in the linear parts of these symmetries when the translation surface has infinite topological type.

  • 14:50 more refreshments for the weary

  • 15:15 Tobias Hartnick, Technion

    Schreiber room 7

    Diffraction theory for aperiodic point sets in Lie groups

    The study of aperiodic point sets in Euclidean space is a classical topic in harmonic analysis, combinatorics and geometry. Aperiodic point sets in R^3 are models for quasi-crystals, and in this context it is of interest to study their diffraction measure, i.e. the way they scatter an incoming laser or x-ray beam.

    By a classical theorem of Meyer, every sufficiently regular aperiodic point set in a Euclidean space is a shadow of a periodic one in a larger locally compact abelian group. The diffraction of these "model sets" can be computed in terms of a certain groups of irrational rotations of an associated torus.

    In recent work with Bjoerklund and Pogorzelski we free model sets from the unnatural corset of abelian groups and consider them in their natural generality, i.e. in the context of arbitrary locally compact groups. This leads to interesting new examples such as (S-)arithmetic quasi-crystals in real and p-adic Lie groups and Burger-Mozes type quasi-crystals in automorphism groups of trees. We develop a general diffraction theory for such point sets, and relate their (spherical) diffraction to the (spherical part of the) automorphic spectrum of the underlying lattice. In our general context, the irrational rotation of the torus gets replaced by an "almost homogeneous dynamical system", i.e. an action of a group G on a space of the form (GxH)/\Gamma for a lattice \Gamma in GxH. The study of diffraction of model sets thus motivates a new kind of "almost homogeneous dynamics", and we will sketch some very modest beginnings of such a theory.

  • You are cordially invited.