# Ben Green

Cambridge University

November 23, 2007 from 16:00 to 18:00 (Montreal/Miami time) On location

Colloquium presented by **Ben Green (Cambridge University)**

Harmonic analysis has proved to be a very effective tool for studying additive questions in number theory. There are many problems, however, for which harmonic analysis does not provide enough information. For some of these problems success has been possible by considering, instead of simply the linear exponentials e^{2 \pi i theta n}, more exotic "harmonics" called nilsequences. The goal of this talk will be to explain (to a general mathematical audience) what nilsequences are, why they are needed, and how they have helped to solve concrete problems concerning primes. In particular we will outline a proof of an asymptotic for the number of quadruples p_1 < p_2 < p_3 < p_4 <= N of primes which lie in arithmetic progression. Joint work with T. Tao.

**Address**