Seminar on homogeneous dynamics and applications

Tel Aviv University, Fall 2016

Time and place Thursday 10:10-12 Kaplun 324 (NOTE CHANGE OF ROOM)

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). This year we will try a mini-course format, with sequences of talks about a particular topic (one or two topics per semester).

  • Nov 4, organizational meeting

    Following the organizational meeting, the topic chosen for the first 6-7 weeks was Veech surfaces (option 2 from the list).

    Here is a list of exercises.

    We will continuously update these as we go along, and add some solutions or hints to exercises we have already discussed.

  • Nov 17-24 , Rene Ruehr, Veech surfaces I

    Definitions of translation surfaces, relation to billiards and interval exchanges, Veech group, definition of Veech surface.

  • Dec 1, Nattalie Tamam, Veech surfaces II

    Arithmetic and non-arithmetic examples, statement of the Veech dichotomy and beginning of proof .

  • Dec 8, Lucia Simonelli

    Some Spectral Methods in Dynamical Systems

    We will explore some common methods in dynamics for proving the existence of absolutely continuous measures in order to illustrate the reliance on exponential decay of correlations. Then we will discuss the difficulties and some methods available for systems that exhibit only polynomial decay of correlations.

  • Dec 15, Nattalie Tamma

    Veech surfaces III

    Proof of the Veech dichotomy, periodic directions.

  • Dec 22, Daniel El-Baz

    Veech surfaces IV

    Masur ergodicity criterion, conclusion of the proof of the Veech dichotomy.

  • Dec 29, Daniel El-Baz Veech surfaces IV (cont.)

    Time permitting, Barak Weiss will discuss non-lattice translation surfaces for which the Veech dichotomy holds, and related open problems.

  • Jan 5, 2017, Yotam Smilansky

    Veech surfaces V

    No small triangles condition

  • Jan 12, Asaf Katz

    Veech surfaces VI

    Smillie's theorem on lattice surfaces and closed orbits, statement of quantitative nondivergence for the horocycle flow on the moduli space of translation surfaces.

  • Jan 26, 2017, Yotam Smilansky

    Veech surfaces VII

    No small triangles condition (continued)

  • Feb 2, 2017, Rene Ruehr

    Veech surfaces VIII

    No small triangles condition (continued). THIS MEETING WILL TAKE PLACE IN SCHREIBER BUILDING ROOM 209

  • Previous years Fall 2014

    Spring 2015

    Fall 2015

    Spring 2016