MATH Seminar

Title: Bounded gaps between primes
Seminar: Joint Athens-Atlanta Number Theory Seminar
Speaker: James Maynard of Universite de Montreal
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2014-02-25 at 5:15PM
Venue: W302
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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 $m\log{m}$. 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.