Math 189-666: Graduate Student Seminar

Organisers: Henri Darmon and Adrian Iovita.

Time: Thursday 8:45-10:15, in BH 920.

This seminar is aimed primarily at the graduate students in the number theory group. The seminar this term will be devoted to the proof of the exceptional zero conjecture of Mazur, Tate, and Teitelbaum by Greenberg and Stevens.

Participants

Kushal Banerjee
Casper Barendrecht
Joachim de Ronde
Michele Fornea
Wissam Ghantous
Francesc Gispert-Sanchez
David Lilienfeldt
Reginald Lybbert
Simone Maletto
Laura Marino
Shayeef Murshid
Kunjakanan Nath
Isabella Negrini
James Rickards
Peter Xu

In addition the following faculty and post-docs will be attending:

Will Chen
Henri Darmon
Adrian Iovita
Zheng Liu
Haining Wang

References. Our three main references will be the following three papers, which belong to the classical canon for people working in Iwasawa theory and p-adic L-functions.

Barry Mazur and Peter Swinnerton-Dyer. Arithmetic of Weil curves. Invent. Math. 25 (1974), 1–61.

Barry Mazur, John Tate, and Jeremy Teitelbaum. On p-adic analogues of the conjectures of Birch and Swinnerton-Dyer. Invent. Math. 84 (1986), no. 1, 1–48.

Ralph Greenberg and Glenn Stevens. p-adic L-functions and p-adic periods of modular forms. Invent. Math. 111 (1993), no. 2, 407–447.

Schedule

1) Classical modular forms and Hecke operators. (Shayeef)

2) Elliptic curves over the rationals and modular forms. The modularity theorem.(Wissam)

3) p-Adic measures on Galois groups and p-adic L-functions. (Isabella)

4) p-Adic L-functions attached to modular eigenforms. The classical theory. (Reginald)

5) The Mazur-Tate-Teitelbaum conjectures. (Michele)

6) Classical and overconvergent modular symbols and the p-adic L-functions attached to modular eigenforms. (Francesc)

7) Galois representations attached to elliptic curves and modular forms. (James)

8) Hida families of ordinary p-adic modular forms and their Galois representations. (David)

9) Two variable p-adic L-functions attached to a Hida family of modular forms. (Peter)

10) The \cL-invariant of an elliptic curve with split multiplicative reduction at p and deformations of Galois representations. (Peter)

11) The proof of the Mazur-Tate-Teitelbaum conjecture for elliptic curves over the rationals with split multiplicative reduction at p. (Michele)

12) Higher weight modular forms (Adrian).