Giovanna De Lauri

Hecke modules associated to some ternary quadratic lattices of discriminant 2p^2

We consider Hecke modules of orthogonal modular forms attached to definite lattices of discriminant 2p^2. With the aid of plenty of examples and by investigating the local structure of such lattices, we will prove explicit Jacquet-Langlands style correspondences with spaces of classical modular forms. Current results on this wider theory will be presented as a survey. We will also provide a state-of-the-art overview of my current research, including both even and odd lattices and ones of discriminant 8p^2.
(Joint work with Dan Fretwell)