Number Theory Seminar: Julia Stadlmann (UIUC)

Title: Bounded gaps between primes  
Abstract: The Polymath project proved that there are infinitely many prime gaps which are no larger than 246. In this talk I will discuss how the Bombieri-Vinogradov theorem can be combined with newer equidistribution estimates for smooth moduli to obtain an improvement on this result. A key ingredient is a new choice of support for the functions appearing in the corresponding optimization problem for the GPY sieve. To choose this support, we produce various equidistribution conditions for moduli with a large smooth factor, and reduce the calculation of relevant integrals to repeated matrix multiplication.