### Monday February 13 , 2006, 4:00 PM

### tea at
3:40 PM at the Math Department lounge (Goldsmith 300)

**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 *p*_{1} < p_{2} < p_{3} < p_{4} <
N which lie in arithmetic progression.