Colloque des sciences mathématiques du Québec

23 novembre 2007 de 16 h 00 à 18 h 00 (heure de Montréal/Miami) Sur place

Nilsequences in Additive Combinatorics

Colloque par 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.


UQAM, Pav. Sherbrooke, 200, rue Sherbrooke O., salle SH-3420