for this workshop
Bounded gaps between primes
American Institute of Mathematics, Palo Alto, California
John Friedlander, Dan Goldston, and Soundararajan
This workshop, sponsored by AIM and the NSF, 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.
The workshop will differ from typical conferences in some regards. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.
The deadline to apply for support to participate in this workshop has passed.
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