Tuesday, June 4th, 2013
2:00pm - 3:00pm, in McCormack 2-116

Yitang Zhang

University of New Hampshire

Bounded Gaps Between Primes

Abstract: Let $p_n$ denote the $n$-th prime. It is proved that $liminf_{n\to \infty} (p_{n+1}-p_n) < 7 x 10^7$. The first step of the proof is to reduce the problem to evaluating and comparing certain arithmetic sums, following the recent work of Goldston, Pintz and Yildirim. Then the major problem we encounter is to bound the error terms efficiently. To this end we introduce a stronger version of the Bombieri-Vinogradov theorem that is motivated by the work of Bombieri, Friedlander and Iwaniec. Some important results in algebraic geometry are needed to complete the proof.