# [Liste-CICMA] Fwd: COLLOQUE CRM-ISM DE MATHÉMATIQUES (21/03/2014, James Maynard)

Dimitris Koukoulopoulos koukoulo at DMS.UMontreal.CA
Wed Mar 19 14:08:35 EDT 2014

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COLLOQUE CRM-ISM DE MATHÉMATIQUES

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DATE :
Le vendredi 21 mars 2014 / Friday, March 21, 2014

HEURE / TIME :
16 h / 4:00 p.m.

CONFERENCIER(S) / SPEAKER(S) :
James Maynard (Université de Montréal)

TITRE / TITLE :
Small gaps between primes

LIEU / PLACE :
CRM, Université de Montréal, pavillon André-Aisenstadt, 2920 chemin de la
Tour, salle 6214

RESUME / ABSTRACT :
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.

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Responsable(s) :
Andrew Granville (andrew at dms.umontreal.ca <javascript:;>)
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http://www.crm.umontreal.ca/Colloques/colloqueMaths.html
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