Seminar on homogeneous dynamics and applications

Tel Aviv University, Spring 2018

Time and place Thursday 11-13 Schreiber 210

About We will amuse ourselves by reading some papers about applications of homogeneous dynamics in number theory (particularly diophantine approximation and geometry of numbers) and geometry of discrete sets (Delone sets). In the fall semester we studied mixing and effective mixing, and in this semester, we will study applications of these results.

  • April 12, Oliver Sargent

    Counting lattice orbits on the upper half plane and counting closed geodesics

    We will follow ideas originating from Margulis' thesis, relating mixing and the count of points in an orbit of lattice orbits on the hyperbolic plane. Some of the ideas can be found in Margulis' thesis ( On some aspects of the theory of Anosov systems ) and some can be found in a survey of Einsiedler and Ward, see section 5.2 of the Durham lecture notes.

  • Tuesday April 24, Rene Ruehr

    Room 210, 14:10

    Counting lattice orbits on affine symmetric space (after Eskin-McMullen)

    The talk will be based on the paper of Eskin and McMullen, "Mixing, counting, and equidistribution in Lie groups", Duke Math. J. Volume 71, (1993), 181-209.

  • Thursday May 3, Rene Ruehr and Arijit Ganguly

    Counting lattice orbits on affine symmetric space (continued)

    This will be a continuation of Rene's talk from last week. Rene will complete his proof of the equidistribution result (theorem 1.2 of the Eskin-McMullen paper) and Arijit will explain how to deduce counting results.

    Here are the notes for Rene's two talks.

  • Thursday May 10, Arijit Ganguly

    Counting lattice orbits on affine symmetric space (continued)

    Arijit will explain the proof of Theorem 1.4 of the Eskin-McMullen paper.

  • Thursday May 17, Yotam Smilansky

    Asymptotic distribution of Frobenius numbers, following J. Marklof

    In the paper The asymptotic distribution of Frobenius numbers, Inventiones Mathematicae 181 (2010) 179-207, Jens Marklof made a connection between a classical problem involving Frobenius numbers, and homogeneous dynamics. Further work on this topic was done by Han Li (see this paper, Compositio Math. 2014 ) and Andreas Strombergsson (see this paper, Acta Arith. 2012 ). In this talk the results will be introduced and the connection to geometry of numbers and homogeneous dynamics will be made.

    Click here for the notes for Yotam's lecture.

  • Wednesday May 23 14:10, room 209, Schreiber building.

    Daniel El-Baz

    Asymptotic distribution of Frobenius numbers (continued)


    The talk will discuss the dynamical ideas behind the proofs of the results of Marklof and Li discussed in Yotam's talk.

  • Wednesday May 30, 14:10 in room 209

    Yiftach Dayan

    Khintchine's theorem and its analogues in homogeneous dynamics


    The talk will state Khintchine's theorem in diophantine approximations, discuss the background and the Borel Cantelli lemma which is the basic tool for proving such results. Then the dynamical interpretation, following Dani, will be presented. The talk will follow the papers "Logarithm laws for flows on homogeneous spaces", by Kleinbock and argulis, Inv. Math. 138 (1999), 451-494, and "Disjoint spheres, approximation by imaginary quadratic numbers, and the logarithm law for geodesics ", by Sullivan, Acta Math. 149 (1982), 215-237. Also lecture notes of Gorodnik will be used.

  • Thursday June 7, Nattalie Tamam

    Khintchine's theorem and its analogues in homogeneous dynamics (continued)

    A continuation of last week's talk with proofs of the divergence case and the connection to quantitative mixing.

  • Previous years Fall 2014

    Spring 2015

    Fall 2015

    Spring 2016

    Fall 2016

    Spring 2017

    Fall 2017