Topics in Ergodic Theory (Brown University, Fall 2010)

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

Lecture notes:

1. Introduction and description of pre-requisites
2. 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