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 \(\liminf_n(p_{n+1}-p_n)\).