MATH Seminar

Title: Elliptic Curves and Moonshine
Defense: Dissertation
Speaker: Maryam Khaqan of Emory University
Contact: Maryam Khaqan, maryam.khaqan@emory.edu
Date: 2021-04-16 at 12:00PM
Venue: https://tinyurl.com/MKhaqan
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Abstract: In this talk, I will describe the main results of my doctoral dissertation. The first main result of my thesis is a characterization of all infinite-dimensional graded modules for the Thompson group whose graded traces are certain weight 3/2 weakly holomorphic modular forms satisfying special properties. This characterization serves as an example of moonshine for the Thompson group.\\ \\ I will begin the talk by giving a brief history of moonshine, describing some of the existing examples of the phenomenon in the literature, and discussing how my work fits into the story. I will then demonstrate how we can use the aforementioned Thompson-modules to study geometric invariants (e.g., rank, p-Selmer groups, and Tate—Shafarevich groups) of certain families of elliptic curves. In particular, this serves as an example of using moonshine answer questions in number theory.\\ \\ Meeting ID: 984 6807 4730 Passcode: 196884