Computer Science/Discrete Mathematics Seminar I | |

Topic: | The Green-Tao theorem and a relative Szemeredi theorem |

Speaker: | Yufei Zhao |

Affiliation: | Massachusetts Institute of Technology |

Date: | Monday, March 3 |

Time/Room: | 11:15am - 12:15pm/S-101 |

Video Link: | https://video.ias.edu/csdm/2014/0303-YufeiZhao |

The celebrated Green-Tao theorem states that there are arbitrarily long arithmetic progressions in the primes. In this talk, I will explain the ideas of the proof and discuss our recent simplifications. One of the main ingredients in the proof is a relative Szemeredi theorem, which says that any subset of a pseudorandom set of integers of positive relative density contains long arithmetic progressions. Our main advance is both a simplification and a strengthening of the relative Szemeredi theorem, showing that a much weaker pseudorandomness condition suffices. I will explain the transference principle strategy used in the proof. Based on joint work with David Conlon and Jacob Fox.