BUNTES is a graduate student-run seminar in Number Theory. Everyone is welcome!

**Time**: Thursday 2pm - 4pm

**Location**: MCS 148

We will treat several topics during the Fall 2018 semester. These are the references we will use for each of them:

** Supersingular Isogeny Graphs and Quaternion Algebras (SIG) **

- Notes by De Feo, Mathematics of Isogeny Based Cryptography
- Kohel's thesis, Endomorphism rings of elliptic curves over finite fields
- Kohel, Lauter, Petit and Tignol, On the quaternion l-isogeny path problem
- Lauter and Petit, Hard and Easy Problems for Supersingular Isogeny Graphs
- Sutherland, Isogeny Volcanoes
- Voight, Quaternion Algebras

** p-divisible Groups and Formal Groups (pFG) **

- Tate, p-Divisible Groups
- Shatz, Chapter 3 in Cornell-Silverman's Arithmetic Geometry
- Feng and Meli, Notes on p-divisible groups
- Dospinescu, Lifting abelian schemes: theorems of Serre-Tate and Grothendieck
- Katz, Serre-Tate Local Moduli
- Youcis, Blog post on the Serre-Tate Theorem

** Shimura Varieties and p-adic Uniformization (SHV) **

- Weinstein, Lecture Notes on Shimura varieties
- Milne, Introduction to Shimura Varieties

There are html and pdf versions of the notes, courtesy of Alex Best.

Date | Topic | Title | Speaker | Notes |

September 6 | SIG | Isogeny Graphs: Background and Motivation | María Inés | Lecture 1 |

September 13 | SIG | Supersingular Isogeny Graphs in Cryptography | Asra | Lecture 2 |

September 20 | SIG | Introduction to Quaternion Algebras | Alex | Lecture 3 |

September 27 | SIG | The Deuring correspondence | María Inés | Lecture 4 |

October 4 | pFG | Introduction to p-Divisible Groups | Sachi | Lecture 5 |

October 11 | SHV | Modular Curves | Aashraya | Lecture 6 |

October 18 | SHV | Modular Forms | Asra | Lecture 7 |

October 25 | SHV | Abelian Varieties and Jacobians | Angus | Lecture 8 |

November 1 | SHV | Hodge Structures | Ricky | Lecture 9 |

November 8 | SHV | Variations of Hodge Structures | Sachi | Lecture 10 |

November 15 | SHV | Hermitian Symmetric Domains | Ricky | Lecture 11 |

November 22 | NO MEETING (Thanksgiving break) | |||

November 29 | SHV | Shimura Varieties | Angus | Lecture 12 |

December 6 | SHV | Alex | Lecture 13 |