# Study group on Roth's Theorem on 3 term arithmetic progressions

In Term 2 2017-18, we are running a study group on Roth's Theorem (1952-53), that any dense subset of the integers must contain a non-trivial 3 term arithmetic progression. The goal is to learn how to prove Roth's Theorem itself, and then to study some variants, for example the analogue in vector spaces over finite fields, and the recent results giving improved quantitative information about the permissible density.

Here is the current schedule of speakers:

Week 1 |
Adam Introduction/history/overview of the proof of Roth's Theorem |

Week 2 |
Marco Proof of Roth's Theorem, part I |

Week 3 |
Alessandro Proof of Roth's Theorem, part II |

Week 4 |
George Roth's theorem in F_{3}^{n}, part I (Meshulam's theorem) |

Week 5 |
Péter Pach Roth's theorem in F_{3}^{n}, part II (the Croot--Lev--Pach theorem) |

Week 6 | No meeting |

Week 7 |
Oleg Pikhurko Roth's theorem in F_{3}^{n}, part III (Upper bounds on the cap-set and sunflower-free problems via slice rank) |

Week 8 |
Josha Improved bounds for Roth's Theorem, part I |

Week 9 |
Mattia Improved bounds for Roth's Theorem, part II |

Week 10 |
Adam Improved bounds for Roth's Theorem, part III |