The group of L. Katzarkov studies themes from classical algebraic geometry (rationality questions, the theory of cycles or Hodge theory) as well as more recent developments such as mirror symmetry. The group of H. Hauser investigates problems from local algebraic and analytic geometry, in particular singularity theory and the resolution of singularities in zero and prime characteristic. Finally, the group of J. Schwermer is interested in varieties which are associated to algebraic groups (module schemes of algebraic varieties, Shimura varieties). Here the main focus is in the connection of representation theory of groups and the geometry.
There are various national and international co-operations within and beyond our field (for instance to commutative algebra, arithmetics or infinity-dimensional geometry). The research is completed by several visualization projects (e.g. the exhibition series Imaginary).