# Small gaps between primes

 Joint IAS/Princeton University Number Theory Seminar Topic: Small gaps between primes Speaker: James Maynard Affiliation: Université de Montréal Date: Thursday, March 6 Time/Room: 4:30pm - 5:30pm/S-101 Video Link: https://video.ias.edu/jointiasnts/2014/0306-JamesMaynard

We will introduce a refinement of the `GPY sieve method' for studying small gaps between primes. This refinement will allow us to show that $\liminf_n(p_{n+m}-p_n) < \infty$ for any integer $m$, and so there are infinitely many bounded length intervals containing $m$ primes. Moreover, this method also applies to any subset of the primes which are reasonably well-distributed in arithmetic progressions. We will also discuss more recent developments from the Polymath project which improve the numerical bounds on $\liminf_n(p_{n+1}-p_n)$.