Previous Special Year Seminar

For the last 5 years or so Terry Tao and I have been working on a programme to prove certain conjectures of Hardy and Littlewood concerning the number of primes vectors p = (p_1, . . . ,p_n) in some box which satisfy the equation Ap = b . The number...

In the first half of the talk I will give details of my joint work with Henryk Iwaniec. We use half-dimensional sieve to obtain a lower bound for the density of rational points on the cubic Chatelet surface. The cubic Chatelet surface can also be...

An overview of methods and results concerning small gaps between primes, between almost primes, and the consequences on values taken by certain arithmetical functions will be presented. The material is from the works with Goldston, Graham and Pintz...

In this mini-course we give a quick tour of sieve methods. The first lecture will deal with the rudiments of the basic theory and mention a few simple examples. The second talk will, for the most part, feature some more recent applications. The...