Speaker: Ben Green (Bristol/Clay/MIT)
Title: Generalising the Hardy-Littlewood method for primes
Abstract: The Hardy-Littlewood method is a technique invented in the 1920s by G.H. Hardy and J.E. Littlewood, building on work of Hardy and Ramanujan. It has many applications to areas such as Waring's problem (every sufficiently large number is the sum of 16 fourth powers, say) and to sums of primes (every large odd number is the sum of three primes).
I will describe recent joint work with T. Tao which is part of a programme to generalise the Hardy-Littlewood so that it can handle more general types of equations in, say, the primes. In particular I will outline our proof of an asymptotic formula for the number of 4-tuples of primes p1 < p2 < p3 < p4 < N which lie in arithmetic progression.