Abelian Varieties and Theta Functions Seminar

Meeting Times: Fridays at 11AM ET / 10AM CST / 8AM PST.

Links to some Texts: Tata Lectures on Theta I, Tata Lectures on Theta II, Tata Lectures on Theta III, Abelian Varieties by Edixhoven, van der Geer, and Moonen

When2Meet Link: https://www.when2meet.com/?19988797-vL52W (Now no longer in use).

Zoom Meeting Link: Here.

Supplementary References:

Tata Lectures on Theta I,II, and III by Mumford (See Mumford's Website for free copies).
Abelian Varieties by Mumford
Curves and their Jacobians by Mumford
Chapter 10 in Stein and Shakarchi's Complex Analysis textbook has a brief summary of applications to number theory.
A Brief Introduction to Theta Functions by Richard Bellman
A First Course in Modular Forms by Diamond and Shurman
Abelian Varieties by Mumford
Arithmetic Geometry by Cornell and Silverman
Abelian Varieties by Edixhoven, van der Geer, and Moonen
Algebraic Number Theory edited by Cassels and Frohlich
The two texts on elliptic curves by Joseph Silverman; The Arithmetic of Elliptic Curves and Advanced Topics in the Arithmetic of Elliptic Curves.
Abelian Varieties and Moduli by Donu Aprodu

Talk Schedule

Meeting 0 May 12, 2023: Logistics + Planning + Talk Plans.

Goals. To study abelian varieties, theta functions, and arithmetic algebraic geometry.

Requirement. Speakers will suggest topics for the next speaker. Talks are typically an hour to an hour and a half long.

Many participants are participating in PAWS 2023. For this reason, some of the last few talks are going to be focused on material from PAWS 2023.

First meeting is May 26th. Kevin Dao. Overview on Abelian Varieties and main results. Slides are posted here.
June 2nd. Shashank Bangalore. Abelian Varieties: Projectivity of Abelian Varieties (Heavily Based off of Math 731 Notes by Bhatt). Slides are posted here.
June 9th. Ryan Tamura. Theta Functions with a View Toward Abelian Varieties. Slides are posted here.
June 16th. Haochen Cheng Tate Curves and p-adic Theta Functions. Slides are posted here.
June 23rd. Jacob Wood. (Jacob is at a conference the week after.) Jacobians and Curves. No slides. The material is covered in Mumford's ``Curves and their Jacobians" Lecture III.
June 30th. Kevin Dao. (Kevin is at a conference the week after.) Heisenberg Groups and Theta Representations. Slides are posted here.
July 7th. Ryan Tamura. Heisenberg Groups and embeddings of Abelian Varieties. Slides are posted here.
July 14th. Haochen Cheng. More on the Dual Variety and Descent. Slides are posted here. Slides are posted here.
July 21st. Ari Davidovsky. Mordell-Weil Theorem based on Silverman's Elliptic Curves Textbook. No slides provided as it was a board talk.
July 28th. Shashank Bangalore. CM Part 1 Based on Ji 2021. Slides are posted here.
August 5th. Cancelled.
August 12th. Ryan Tamura. An Overview of CM Elliptic Curves with a focus towards potential good reduction. Slides are posted here.
August 19th. Kevin Dao. Moduli of Abelian Varieties. Slides are posted here.
August 26th. Haochen Cheng. (Canceled due to flight delays.) The talk would have been about the following notes: Moduli of abelian varieties and p-divisible groups by Ching-Li Chai and Frans Oort.