Gaps between primes

This workshop, sponsored by AIM and the NSF, will be devoted to the recent work of Goldston, Pintz, and Yildirim on gaps between primes and primes in tuples. The work depends on a surprisingly effective variation of the Selberg sieve, and it has connections and applications to other problems in sieve methods. We seek participants who are experts in sieve methods as well as those who are not; in particular, we encourage those who may be unfamiliar with sieves but have expertise in other areas of number theory to attend. The simplicity of the basic ideas should allow the participants to quickly understand both what is known and what are the main unresolved questions. Further applications and relationships to other areas of number theory will be explored. The main topics for the workshop are:

• Approximations for primes in tuples and their application to small gaps between primes
• Applications of the new approximations to sieve methods, numbers with few prime factors, and the parity problem
• Open problems such as bounded gaps between primes, level of distribution of primes in arithmetic progressions, the relationship between the Elliott-Halberstam conjecture and the twin prime conjecture, and further applications to other problems.

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 working sessions.

The deadline to apply for support to participate in this workshop has passed.

For more information email workshops@aimath.org

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