#
Bounded gaps between primes

November 17 to November 21, 2014
at the

American Institute of Mathematics,
Palo Alto, California

organized by

John Friedlander,
Dan Goldston,
and Soundararajan

## Original Announcement

This workshop will focus on the remarkable progress made in the last year on
gaps between prime numbers. The breakthrough result of Zhang first established
that there are bounded gaps between consecutive primes, and this was quickly
followed by another extraordinary argument by Maynard (and discovered
independently by Tao), establishing the existence of many primes in bounded
intervals. Both results start from a method pioneered by Goldston, Pintz and
Yildirim, but
then proceed in very different directions. Zhang's breakthrough is based on
an
extension of the Bombieri-Vinogradov theorem (building on earlier work of Fouvry
and Iwaniec, and Bombieri, Friedlander and Iwaniec), while
Maynard's work re-examines the classical sieve method of Selberg and finds an
astonishingly strong variant.
The workshop will discuss the ideas behind these breakthrough results, and
explore possible applications to other problems. The classical
Bombieri-Vinogradov theorem has numerous pplications, and one may hope that the
partial extension of Zhang will also have more consequences. Likewise, the
Selberg sieve is ubiquitous in number theory, and it would be worth exploring
the flexibility of the weights in Maynard's work. Another natural focus of
the workshop will be on obtaining sharper versions of the results of Zhang and
Maynard, taking into account the subsequent improvements by
Polymath and perhaps others, and on understanding the limitations of these
methods. The workshop will bring together senior researchers in analytic number
theory, sieve methods, additive
combinatorics, together with many promising young researchers in these and
related areas.

## Material from the workshop

A list of participants.
The workshop schedule.

A report on the workshop activities.

Papers arising from the workshop: