2024 Program for Women+ and Mathematics

Modular Generating Series for Real Quadratic Heegner Objects

Abstract: The theory of elliptic curves with complex multiplication has yielded some striking arithmetic applications, ranging from (cases of) Hilbert’s Twelfth Problem to the Birch and Swinnerton-Dyer Conjecture. These applications rely on the construction of certain “Heegner objects”, arising from imaginary quadratic points on the complex upper half plane; the most famous examples of these are Heegner points. 

In recent years, conjectural analogues of these Heegner objects for real quadratic fields have been constructed via p-adic methods. In this talk, I will discuss how Heegner objects for real quadratic fields can be used to obtain modular generating series, that is, formal q-series that are q-expansions of classical modular forms. This is joint work with Judith Ludwig, Isabella Negrini, Sandra Rozensztajn and Hanneke Wiersema. 

Date & Time

May 23, 2024 | 5:15pm – 5:55pm

Location

Simonyi Hall 101

Speakers

Alice Pozzi, University of Bristol

Event Series

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