Seminar on Topics in Arithmetic, Geometry, Etc.

STAGE is a seminar in algebraic geometry and number theory, featuring speakers talking about work that is not their own. Talks will be at a level suitable for graduate students. Everyone is welcome.
Meetings are held on Wednesdays, 10am-11:30 currently virtually via a zoom videoconference.
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If you are interested in giving one of the talks, please contact the organizers.

Spring 2020 topic: p-adic modular forms.

References to be followed:

Serre, Formes modulaires et fonctions zeta p-adiques, Chapter 1: pp. 191-205 in Modular Functions of One Variable III, Springer Lecture Notes in Mathematics 350 (1973).
Katz, p-adic properties of modular schemes and modular forms: pp. 69-190 in Modular Functions of One Variable III, Springer Lecture Notes in Mathematics 350 (1973). We expect to cover up to Section 3.9.
Katz, p-adic L-functions for CM fields, Invent. Math. 49 (1978), no. 3, 199-297.

Other references:

Calegari, 2013 Arizona Winter School lecture notes. This is an excellent overview of the overall topic.
Katz, p-adic interpolation of real analytic Eisenstein series. Ann. of Math. (2) 104 (1976), no. 3, 459-571. Chapters I, II, V contain a nice review of much of the material of Katz 1973.

Some topics below might take more or less time than allotted. If a speaker runs out of time on a certain date, that speaker might be allowed to borrow some time on the next date. So the topics below might not line up exactly with the dates below.

February 5: Samuel Marks. p-adic modular forms à la Serre. Serre, Chapter 1. (notes)

February 12: Naomi Sweeting. Modular Forms from a Geometric Perspective. Katz 1973, Sections 1.1-1.6.

February 19: Borys Kadets. Modular schemes and Hecke operators. Katz 1973, Sections 1.7-1.13.

February 26: Murilo Corato Zanarella. p-adic modular forms à la Katz. Katz 1973, Chapter 2. (notes)

March 4: Yifan Wu. The canonical subgroup. Katz 1973, Chapter 3 up to Section 3.9 inclusive.

March 11: NO SEMINAR (Arizona Winter School)

March 18: Alex Best. Motivation from complex analysis; Gauss-Manin connection. Katz 1973, Appendix 1.

March 25: NO SEMINAR (Spring Break)

April 1: Zhiyu Zhang. Frobenius on p-adic modular forms and the theta operator. Katz 1973, Appendix 2.

April 8: Si Ying Lee. Modular forms on Hilbert modular varieties. Katz 1978, Sections 1.0-1.8.

April 15: Alexander Petrov. p-adic modular forms on Hilbert modular varieties. Katz 1978, Sections 1.9-1.12.

April 22: Tony Feng. Differential operators on modular forms. Katz 1978, Sections 2.0, 2.1, 2.5, 2.6.

April 29: Ziquan Yang. p-adic Eisenstein series. Katz 1978, Sections 3.2 and 3.4.

May 6: Zijian Yao. CM Hilbert-Blumenthal abelian varieties. Katz 1978, Sections 5.0 and 5.1, and the statements of 5.2.26 and 5.2.29.

May 13: Daniel Kriz. Construction of Katz p-adic L-functions. Katz 1978, Chapter 4 and Sections 5.3 and 5.4.

Past semesters: Fall 2009, Spring 2010, Fall 2010, Spring 2011, Fall 2011, Spring 2012, Fall 2012, Spring 2013, Fall 2013, Spring 2014, Fall 2014, Spring 2015, Fall 2015, Spring 2016, Fall 2016, Spring 2017, Fall 2017, Spring 2018, Fall 2018, Spring 2019, Fall 2019

Organizers: Daniel Kriz, Bjorn Poonen, Zhiyu Zhang