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Lie Group Quantum Mathematics Seminar

Moonshine and Elliptic Curves

Maryam Khaqan, Stockholm University

Date & time: Friday, 12 November 2021 at 11:00AM - 12:00PM

Abstract: The study of moonshine originated from a series of numerical coincidences connecting finite groups to modular forms. It has since evolved into a rich theory that sheds light on the underlying algebraic structures that these coincidences reflect.

We prove the existence of one such structure, a module for Thompson's sporadic simple group, whose graded traces are specific half-integral weight weakly holomorphic modular forms. We then use this module to study the ranks of certain families of elliptic curves. In particular, this serves as an example of moonshine being used to answer questions in number theory.

Zoom link
Meeting ID: 939 2146 5287
Passcode: 196884, the dimension of the weight 2 homogeneous
subspace of the moonshine module

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