NTAG Seminar: Modular generating series for real quadratic Heegner objects

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.