Ergodic Theory

This is the webpage for my Lent 2008 Part III course on Ergodic Theory, which meets at 10am on Monday, Wednesday and Friday in MR13. Full printed notes will be produced: students are also entreated to make regular visits to Terry Tao's Blog.

0: Introduction to the course

1: Van der Waerden's theorem by topological dynamics

2: More topological dynamics -- distribution of polynomials modulo one

3: Introduction to ergodic theory. Ergodic theorems

4: Applications of the ergodic theorems

5: Ergodicity, unique ergodicity and group extensions

6: The Furstenberg-Sarkozy Theorem

7: Szemeredi's theorem: the weak-mixing case

8: Szemeredi's theorem: the compact case

9: Szemeredi's theorem: a study of the skew torus

10: Szemeredi's theorem: a sketch of the rest of the proof

11: Orbits on the Heisenberg nilmanifold

A1: A very brief introduction to measure theory

A2: A primer on conditional expectation

E1: Examples 1

E2: Examples 2

0: Introduction to the course
1: Van der Waerden's theorem by topological dynamics
2: More topological dynamics -- distribution of polynomials modulo one
3: Introduction to ergodic theory. Ergodic theorems
4: Applications of the ergodic theorems
5: Ergodicity, unique ergodicity and group extensions
6: The Furstenberg-Sarkozy Theorem
7: Szemeredi's theorem: the weak-mixing case
8: Szemeredi's theorem: the compact case
9: Szemeredi's theorem: a study of the skew torus
10: Szemeredi's theorem: a sketch of the rest of the proof
11: Orbits on the Heisenberg nilmanifold
A1: A very brief introduction to measure theory
A2: A primer on conditional expectation
E1: Examples 1
E2: Examples 2