Number Theory Seminar - Spring 2021

p-adic Modular Forms and p-adic L-functions


Description
I organised an online seminar on p-adic modular forms and p-adic L-functions at Columbia University. It 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.
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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.
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Schedule
Date Title Speaker Reference Notes
Jan. 26 Motivation : On Congruences of Modular Forms David Marcil [H2], [Sh] PDF
Feb. 02 Kubota-Leopoldt p-adic L-functions Baiqing Zhu [H1], [W] PDF
Feb. 09 Overview of Iwasawa Theory Yu-Sheng Lee [W], [Sk] PDF
Feb. 16 Eichler-Shimura isomorphism, ordinary modular forms and Hida family (I) Hung Chiang [H1] PDF
Feb. 23 Eichler-Shimura isomorphism, ordinary modular forms and Hida family (II) Hung Chiang [H1] PDF
Mar. 02 Spring Break - No Lecture
Mar. 09 \Lambda-adic Galois representations Avi Zeff [H1] PDF
Mar. 16 p-adic Properties of Modular Schemes and Modular Forms Haodong Yao [K] PDF
Mar. 23 Mazur-Swinnerton-Dyer p-adic L-functions Michele Fornea PDF
Mar. 30 Overconvergent Modular Forms David Marcil [C], [V] PDF
Apr. 06 Overconvergent Modular Symbols David Marcil [PS] PDF
Apr. 13 The Coleman-Mazur Eigencurve : A Survey Samuel Mundy [CM] PDF
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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