Abel Castillo : Bounded gaps between primes and applications of the Maynard-Tao method

Posted by Cara Mullen , part of the Graduate Number Theory Seminar.

At

Sept. 15, 2014, 3 p.m.

In

SEO 712

Abstract

The Twin Prime Conjecture asks if there are infinitely many primes $p$ such that the next prime $p_{next}$ satisfies $p_{next} - p=2$. In this talk we will survey recent results towards this conjecture, where one finds infinitely many primes $p$ such that $p_{next} - p$ is much smaller than average. We will then give an overview of the sieve used by Goldson-Pintz-Yilidrim, which was the foundation of the work on bounded gaps between primes by Zhang and Maynard-Tao. Finally, we will mention variants of the Maynard-Tao method that give bounded gaps between primes with properties of arithmetic interest.