Faculty Sponsor: Fan Chung.

Location: AP&M 6436 (Combinatorics Office, for now)

Time: M 12pm

The seminar is now over. Some of us will be working on related problems this winter (07). If you want to find out what we're doing, send an email to the organizers. This page will remain up for a while as a reference.

This is a reading course for Fall '06 (perhaps to continue in the winter) designed to learn methods of harmonic analysis (continuous and finite field) which are used in the study of combinatorics and additive number theory. Applications of this method are very much in vogue these days, and include the monumental work of Gowers on Szemerédi's theorem and Green-Tao on arithmetic progressions in the primes (that's two fields medalists and one Clay research fellow in a single sentence). Much recent progress has appeared in related problems, such as incidence (Szemerédi-Trotter) geometry, Kekaya problems, and distance sets.

Our goal is to learn the basic language of harmonic analysis in as much as it relates to these problems. We shall also touch on probabilistic methods and quasirandomness and try to discover how these fields intertwine. The thrust of the course will be determined by the interest and background of the participants. If all goes well, we may attempt a more problem-focused reading course in the winter. Combinatorists involved in Hungarian/probabilistic methods will find much here for them. Number theorists looking to learn harmonic analysis may also benefit (perhaps while reading Montgomery). Analysts may also find something of interest. All participants are expected to participate, and the format is expected to be a mixture of discussion and short presentation. Course credit may be available.

- Quasi-Random Subsets of Z_n. We will discuss 10/02.
- Quasirandomness, Counting, anad Regularity for 3-Uniform Hypergraphs.
- A new proof of Szemerédi's theorem.
- Quadratic Fourier Analysis. (maybe)
- Exponential sums reference.
- Graph Products, Fourier Analysis and Spectral Techniques.

- Gower's Website.
- A similar course by Laba.
- A course by T. Tao.
- A course by V. Vu.
- Ben Green's website.
- Harmonic Analysis by Wolff.
- Additive Combinatorics (Tao and Vu)
- Open Problems in Additive Combinatorics.
- Combinatorics of Patterns, Lecture notes from math262.
- A course by Peter Keevash.
- Additive number theory : inverse problems and the geometry of sumsets / Melvyn B. Nathanson (In Library)
- Ten lectures on the interface between analytic number theory and harmonic analysis / Hugh L. Montgomery (In Library)
- Additive Combinatorics, Tao and Vu.
- Dinur and Friedgut's class.
- Harmonic Analysis of Boolean Functions.
- Gowers' Additive Number Theory Notes. A good exposition on Weyl's inequality.