Our general research interests lie in the realms of global differential geometry, Riemannian geometry, geometric topology, and their applications.
Current topics under investigation include, e.g., questions concerning the geometry and topology of nonnegative and almost nonnegative curvature, singular metric spaces, collapsing and Gromov-Hausdorff convergence, analysis and geometry on Alexandrov spaces, geometric finiteness theorems, moduli spaces of Riemannian metrics, transformation groups, geometric bordism invariants, information and quantum information geometry.
Jointly with the research groups Metric Geometry, Topology, Applied Analysis and Number Theory & Algebraic Geometry we constitute the Forschungsschwerpunkt Geometry, Groups and Topology. Our research group also participates in the Forschungsschwerpunkt Partielle Differentialgleichungen and the DFG-Graduiertenkolleg 1194 Self-organizing Sensor-Actuator-Networks.
Moduli Spaces of Riemannian Metrics
Oberwolfach, June 8-14, 2014
Riemannian Topology Seminar
F-Structures in Geometry and Topology
Karlsruhe, November 28-29, 2013
Geometry, Groups and Topology 2013
Karlsruhe, October 7-11, 2013