This is the webpage for my Lent 2009 Part III course on Additive Combinatorics, which meets at 11am on Monday, Wednesday and Friday in MR5. Full printed notes will be produced.
Recommended reading: Tao and Vu's book is a comprehensive reference text. My review of this book for the Bulletin of the AMS serves as well as anything as an introduction to the course. Other further reading will have attention drawn to it as we go along.
| 1: Roth's Theorem on progressions of length 3 |  |
| 2: Sumsets | |
| 3: Small doubling and the Freiman-Ruzsa theorem | |
| 4: The Balog-Szemeredi-Gowers theorem | |
| 5: Longer progressions and higher Gowers norms | |
| 6: Sum-product theory over F_p | article |
| 7: The sum-product phenomenon over C | |
| E1: Examples 1 | |
| E2: Examples 2 | |