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Large gaps between primes in subsets

Recent developments in Analytic Number Theory May 01, 2017 - May 05, 2017

May 04, 2017 (03:30 PM PDT - 04:30 PM PDT)
Speaker(s): James Maynard (University of Oxford)
Location: MSRI: Simons Auditorium
Tags/Keywords
  • primes in polynomials

  • density of primes

  • small gaps between primes

  • sieve methods

  • consecutive composites in polynomials

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

Abstract

All previous methods of showing the existence of large gaps between primes have relied on the fact that smooth numbers are unusually sparse. This feature of the argument does not seem to generalise to showing large gaps between primes in subsets, such as values of a polynomial. We will talk about recent work which allows us to show large gaps between primes without relying on smooth number estimates. This then generalizes naturally to show long strings of consecutive composite values of a polynomial. This is joint work with Ford, Konyagin, Pomerance and Tao

Supplements
28401?type=thumb Maynard Notes 1.06 MB application/pdf Download
Video/Audio Files

Maynard

H.264 Video 13-Maynard.mp4 592 MB video/mp4 rtsp://videos.msri.org/data/000/028/330/original/13-Maynard.mp4 Download
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