**Some highlights of arithmetic combinatorics**

**MW 3-4:30, MS 6221
**

**Terence Tao, tao@math.ucla.edu,
x64844, MS 5622
**

Lecture notes:

- Lecture notes 1: Cauchy-Davenport inequality, Plunnecke's theorem, sum set estimates. Errata to Q2: |A|, |B| need to be assumed to be at least 2. Errata to Q10(a): "translates of B" should read "translates of B-B". Errata to Q11: "and some subset A' such that |A'| >= (1-delta) |A| and" should read "such that for every subset A' with |A'| >= (1-delta)|A|, we have". Thanks to Roman Sasyk for pointing out these errata.
- Lecture notes 2: Freiman's theorem (both in
the torsion and torsion-free cases), Gowers-Walters theorem, Chang's
refinement of Freiman's theorem

- Lecture notes 3: Gowers' quantitative Balog-Szemeredi theorem; applications to the Kakeya problem; applications to a multilinear convolution integral. Errata to Q4: The theorem as stated is false; it is best to forget this question entirely.
- Lecture notes 4: Roth's theorem for APs of length 3; Gowers' proof of Szemeredi's theorem for APs of length 4.
- Lecture notes 5: Behrend's example; Bourgain's refinement of Roth's theorem.
- Lecture notes 6: Crossing numbers and Szemeredi's theorem; Elekes's sum-product theorem; Bourgain-Katz-Tao sum-product theorem; finite field Szemeredi-Trotter and distance set problem results.

- The
web page of Ben Green, including his
lecture notes on Freiman's theorem.

- The web page of Tim Gowers.
- The web page of Imre Ruzsa.
- Van
Vu's grad course home page on combinatorial number theory (a course
running in parallel with ours wich much overlap of topics, but a
different mathematical perspective).