Description

I organised an online seminar on p-adic modular forms and p-adic L-functions at Columbia University. It is focused on the theory of p-adic modular forms. It is mostly arithmetically inclined but the geometric point of view is still relevant. Some topics included (in no particular order) are : Hida families, p-adic L-functions, overconvergent modular forms, Iwasawa theory, Stark-Heegner points and computational aspects of the theory.
Relevant information

Time: Tuesday, 10:00AM-11:15AM (Eastern Time) Zoom Meeting ID : 917 3408 7965.

Password : Constant term in q-expansion of the modular j-function.

Schedule

Date | Title | Speaker | Reference | Notes |
---|---|---|---|---|

Jan. 26 | Motivation : On Congruences of Modular Forms |
David Marcil | [H2], [Sh] | |

Feb. 02 | Kubota-Leopoldt p-adic L-functions |
Baiqing Zhu | [H1], [W] | |

Feb. 09 | Overview of Iwasawa Theory |
Yu-Sheng Lee | [W], [Sk] | |

Feb. 16 | Eichler-Shimura isomorphism, ordinary modular forms and Hida family (I) |
Hung Chiang | [H1] | |

Feb. 23 | Eichler-Shimura isomorphism, ordinary modular forms and Hida family (II) |
Hung Chiang | [H1] | |

Mar. 02 | Spring Break - No Lecture |
|||

Mar. 09 | \Lambda-adic Galois representations |
Avi Zeff | [H1] | |

Mar. 16 | p-adic Properties of Modular Schemes and Modular Forms |
Haodong Yao | [K] | |

Mar. 23 | Mazur-Swinnerton-Dyer p-adic L-functions |
Michele Fornea | ||

Mar. 30 | Overconvergent Modular Forms |
David Marcil | [C], [V] | |

Apr. 06 | Overconvergent Modular Symbols |
David Marcil | [PS] | |

Apr. 13 | The Coleman-Mazur Eigencurve : A Survey |
Samuel Mundy | [CM] |

References

[C] Calegari, Frank - Congruence Between Modular Forms

[CM] Coleman, R. Mazur, B. - The Eigencurve

[H1] Hida, Haruzo - Elementary Theory of L-functions and Eisenstein Series

[H2] Hida, Haruzo - Congruences of Cusp Forms and Special Values of L-functions

[K] Katz, Nicholas M. - p-adic Properties of Modular Schemes and Modular Forms

[PS] Pollack, R. Stevens, G. - Overconvergent Modular Symbols

[Sh] Shimura, Goro - Introduction to Arithmetic Theory of Automorphic Functions

[Sk] Skinner, Christopher - Galois Representations, Iwasawa Theory, and Special Values of L-functions

[V] Vonk, J. - Overconvergent Modular Forms and Their Explicit Arithmetic

[W] Washington, Lawrence C. - Introduction to Cyclotomic Fields