Titel: Computing Hilbert modular forms and tables of elliptic curves
Abstract: Hilbert modular forms are a generalization of ordinary modular forms, in which the role of GL_2(Z) is taken by GL_2(Z_K), where Z_K is the ring of integers in a (totally real) number field. This is a close generalization: in particular, the celebrated 'Modularity Theorem' of Wiles et al has been extended to this setting, which tells us that elliptic curves over such fields correspond to modular forms in a precise way.
After introducing all these things, I will survey work done by myself and others during the last few years which makes it possible to compile tables of modular forms and elliptic curves over many number fields.. This work includes several approaches to calculating modular forms with their Hecke action, as well as techniques for finding equations of the corresponding elliptic curves.