ACTION NOW WANDERING SEMINAR

Third meeting, Technion, 15.5.18, Amado Building room 232


  • 10:00 Tali Pinsky, Technion

    An upper bound for volumes of geodesics

    Consider a closed geodesic gamma on a hyperbolic surface S, embedded in the unit tangent bundle of S. If gamma is filling its complement is a hyperbolic three manifold, and thus has a well defined volume. I will discuss how to use Ghys' template for the geodesic flow on the modular surface to obtain an upper bound for this volume in terms of the length of gamma. This is joint work with Maxime Bergeron and Lior Silberman.

  • 11:10 Anish Ghosh, Tata Institute, Mumbai

    The metric theory of dense lattice orbits

    Abstract: The classical theory of metric Diophantine approximation is very well developed and has, in recent years, seen significant advances, partly due to connections with homogeneous dynamics. Several problems in this subject can be viewed as particular examples of a very general setup, that of lattice actions on homogeneous varieties of semisimple groups. The latter setup presents significant challenges, including but not limited to, the non-abelian nature of the objects under study. In joint work with Alexander Gorodnik and Amos Nevo, we develop the first systematic metric theory for dense lattice orbits, including analogues of Khintchine's theorems.

  • 12:00 Lunch and informal discussions

  • 14:00 Konstantin Golubev, Bar Ilan and Weizmann Institute

    Density theorems and almost diameter of quotient spaces

    We examine the typical distance between points in various quotient spaces. This question has an interesting approach inspired by the work of Lubetzky and Peres. They showed that the random walk on a graph expresses under the assumption of the graph being Ramanujan. We show that this condition can be relaxed to some density condition on the eigenvalues, and apply it to various settings. Joint work with Amitay Kamber.

  • 15:10 Sanghoon Kwon, Korea Institute for Advanced Study

    The set of critical exponents of discrete groups acting on regular trees

    We study the set of critical exponents of discrete groups acting on regular trees. We prove that for every real number x between 0 and 1/2(log q), there is a discrete subgroup acting on a (q+1)-regular tree whose critical exponent is equal to x. We also investigate the critical exponents of Schottky free discrete groups of rank 2 and give minimal polynomials of some examples.

  • You are cordially invited.

    A PARKING PERMIT FOR ALL PARTICIPANTS HAS BEEN ARRANGED. AT THE GATE, SAY YOU ARE ATTENDING THE ACTION NOW MEETING.