Welcome to the Fall 2019 page for the Boston University Number Theory Expository Seminar! For previous years' seminars, see Angus's website.

Our topic for Fall 2019 semester was Gross Zagier. We met weekly and took turns giving lectures on various topics.

Some good references: On On Singular Moduli; Heegner points and derivatives of L-series (the main reference); Heegner Points and Derivatives of L-Series II, and the pair of Zagier articles for an overview, Modular Points, Modular Curves, Modular Surfaces, and Modular Forms, L-Series and the Green's Functions of Modular Curves . For Kolyvagin's work, see the Rubin article The work of Kolyvagin on the arithmetic of elliptic curves as well as Gross's article.

Some other seminars on Gross Zagier in the past include Harvard 2013, Michigan 2014 and Oxford 2018.

**Time**: Tuesday 9am - 11am

**Location**: B39

Week | Topic | Speaker | Notes |

1 (9/9-9/13) | Introduction/Overview | Sachi | Notes by Alex |

2 (9/16-9/20) | Modular Curves Background I | John | Notes by Sachi Notes by Alex |

3 (9/23-9/27) | Modular Curves Background II | Ricky | Notes by Sachi |

4 (9/30-10/4) | Archimedean Local Heights I | Aash | Notes by Sachi Notes by Alex |

5 (10/7-10/11) | Archimedean Local Heights II | Stevan | Notes by Alex |

(10/14-10/18) | NO BUNTES (BU Monday) | ||

6 (10/21-10/25) | Deuring's theory of lifts of elliptic curves | Angus | Notes by Alex |

7 (10/28-11/1) | Deformation theory of elliptic curves (Serre-Tate) | Alex | Notes by Sachi |

8 (11/4-11/8) | Non Archimedean Local heights | Oana | Notes by Oana |

9 (11/11-11/15) | Wrap up of Non Archimedean local heights | Sachi | Notes by Alex |

10 (11/18-11/22) | Rankin L-Series | Aash | Notes by Alex |

11 (11/25-11/29) | Applications of Heegner Points | Alex | Notes by Sachi Notes by Alex |

12 (12/2-12/6) | Applications of Heegner Points (cont.) | Alex | Notes by Alex |

13 (12/9-12/13) Special time: 10am - 12pm |
Kolyvagin's work | Oana and John | Notes from Oana Notes from John |