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