PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Robert Vaughan, Karl Schwede, Mihran Papikian, Ae Ja Yee.

Title:Small gaps between primes
Seminar:Algebra and Number Theory Seminar
Speaker:James Maynard, Centre de recherches mathématiques
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.

Room Reservation Information

Room Number:MB106
Date:02 / 06 / 2014
Time:11:15am - 12:05pm