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.