Dynamics on moduli spaces of translation surfaces

Tel Aviv University, Fall 2025


Grading Grades will be based on this exercise sheet. If you are taking the course for a grade, or if you just wanna have fun, solve as many as you can. If you are getting help from others or from books or LLMs, give appropriate credit. Due date is after the end of the semester (precise date will be given later).


Lectures Monday 9:10-12, Dan David 103. Lectures will be broadcast by zoom, the zoom broadcast and recordings are available through the TAU Moodle system.

If you want to access zoom and do not have TAU Moodle access, please contact me.




Notes In the lecture of December 1 I skipped the proof of the following lemma.




Books
  • J. Athreya and H. Masur, Translation surfaces
    (a recent general introduction to the topic).

  • G. Forni and C. Matheus, Introduction to Teichmueller theory and its applications to interval exchange transformations, flows on surfaces and billiards
    (a detailed survey).

  • M. Viana, Dynamics of interval exchange transformations and Teichmueller flows
    (a detailed survey).

  • R. Schwartz, Mostly surfaces
    (a more elementary textbook covering many aspects of surface geometry and topology).

  • M. Einsiedler and T. Ward, Ergodic Theory: With a View Towards Number Theory
    (a general introduction to ergodic theory and dynamical systems).

  • B. Hasselblatt and A. Katok, Introduction to the Modern Theory of Dynamical Systems
    (another good general introduction).

  • A. Hatcher, Algebraic topology
    (a general introduction to relevant notions from algebraic topology).

  • W. Goldman, Geometric structures on manifolds
    (a general introduction to relevant geometric notions).