Thursday, September 14
Time: 4:00 p.m.
Location: 114 McAllister Building
Name: D. Goldston
Affiliation: San Jose State University
Title: Small Gaps Between Primes
Abstract: I will talk about recent joint work with Janos Pintz and Cem Yildirim on small gaps between primes. A surprising result of our work is that if the primes are well distributed in arithmetic progressions then one can prove results not too far from the twin prime conjecture. For example, if the Elliott-Halberstam conjecture is true then there are infinitely many pairs of primes with difference 16 or less. Unconditionally we can prove a long-standing conjecture in the field: there are pairs of primes much closer together than the average distance between consecutive primes.
This work has had its share of media attention, and even generated a song on public television. For me there has been three stages to this publicity: the enjoyment of small-time public fame for proving the result three years ago, followed closely by the unenjoyable publicity when Granville and Soundararajan showed how the proof crashed and burned beyond repair, and lastly the redemption following the strange emergence of a new proof. After Wiles this may seem like standard procedure in mathematics, but I would not recommend it for the faint of heart.