Colloque des sciences mathématiques du Québec

21 mars 2014 de 16 h 00 à 18 h 00 (heure de Montréal/Miami) Sur place

Small gaps between primes

Colloque par 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.

Adresse

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