For more information about this meeting, contact Robert Vaughan, Karl Schwede, Mihran Papikian, Ae Ja Yee.

Title: | Small gaps between primes |

Seminar: | Algebra and Number Theory Seminar |

Speaker: | James Maynard, Centre de recherches mathÃ©matiques |

Abstract: |

It is believed that there should be infinitely many pairs of primes which differ by 2; this is the famous twin prime conjecture. More generally, it is believed that for every positive integer $m$ there should be infinitely many sets of $m$ primes, with each set contained in an interval of size roughly $m\log{m}$. Although proving these conjectures seems to be beyond our current techniques, recent progress has enabled us to obtain some partial results. We will introduce a refinement of the `GPY sieve method' for studying these problems. This refinement will allow us to show (amongst other things) that $\liminf_n(p_{n+m}-p_n)<\infty$ for any integer $m$, and so there are infinitely many bounded length intervals containing $m$ primes. |

### Room Reservation Information

Room Number: | MB106 |

Date: | 02 / 06 / 2014 |

Time: | 11:15am - 12:05pm |