This graduate-level course consisted of 12 lectures of 1.5 hours each.

Lecture notes:

1. Introduction and description of pre-requisites2. The Ergodic Theorems

3. Topological systems and equidistribution

4. Mixing and the `arithmetic' of systems

5. More about mixing

6. Introduction to Szemeredi's Theorem and Multiple Recurrence

7. Multiple Recurrence II: convergence of nonconventional averages

8. Multiple Recurrence III: structure of the Furstenberg self-joining

9. Multiple Recurrence IV: completing the proof of multiple recurrence

10. Introduction to entropy

11. More about entropy

12. Proof of Sinai's Theorem

Problem sheets:

Sheet 1.Sheet 2. (With correction from the hardcopies in class: the base-2 log in Qu. 6(a) should be a natural log).

Sheet 3.

Sheet 4.

Tim Austin,

Courant Institute of Mathematical Sciences, New York University

New York, NY 10012, U.S.A.

tim AT cims DOT nyu DOT edu