Linear equations in primes

4 May 2007
Professor Ben Green
I shall report on a programme of research which is joint with Terence Tao. Our goal is to count the number of solutions to a system of linear equations, in which all variables are prime, in as much generality as possible. One success of the programme so far has been an asymptotic for the number of four-term arithmetic progressions p_1 < p_2 < p_3 < p_4 <= N of primes, defined by the pair of linear equations p_1 + p_3 = 2p_2, p_2 + p_4 = 2p_3. The talk will be accessible to a general audience.