Quebec Mathematical Sciences Colloquium

March 21, 2014 from 16:00 to 18:00 (Montreal/Miami time) On location

Small gaps between primes

Colloquium presented by James Maynard (University of Oxford)

It is believed that there should be infinitely many pairs of primes which differ by 2; this is the famous twin prime conjecture. More generally, it is believed that for every positive integer $m$ there should be infinitely many sets of $m$ primes, with each set contained in an interval of size roughly $m\log{m}$. Although proving these conjectures seems to be beyond our current techniques, recent progress has enabled us to obtain some partial results. We will introduce a refinement of the `GPY sieve method' for studying these problems. This refinement will allow us to show (amongst other things) 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.


CRM, Université de Montréal, pavillon André-Aisenstadt, 2920 chemin de la Tour, room 6214