John Voight (Vermont)
Computing automorphic forms on Shimura curves
Modular symbols allow a detailed investigation of classical modular
forms. Automorphic forms on more general Shimura varieties have
proved no less interesting to study, and yet many aspects of the
theory are not as well understood. In joint work with Matt Greenberg,
we present an algorithm to compute automorphic forms on Shimura curves
working with explicit group cohomology; via the Jacquet-Langlands
correspondence, these methods also allow the computation of Hilbert
modular forms over totally real fields of odd degree. Our
methods work without reference to cusps or a canonical moduli
interpretation of the Shimura curve, as these features of the
classical situation are absent.