Research Projects of Matthias Schütt

In several projects the group explores the connections of geometry and arithmetic. The main objects of study in this context are algebraic surfaces, Calabi-Yau threefolds and irreducible holomorphic symplectic manifolds. Notably, we investigate K3 surfaces with high Picard number or automorphisms. There are close connections with modular forms, class group theory, and Shimura varieties. In this context elliptic fibrations play an important role. For Calabi-Yau threefolds we have achieved several results on modularity. Currently our focus lies on the development of new constructions and their connections to string theory. (Schütt et al.)