The research areas and interests of the Differential Geometry Research Group concern questions in global differential geometry, Riemannian geometry, geometric topology, and their applications.

Current research topics include, among others, the geometry and topology of nonnegative and almost nonnegative curvature, singular metric spaces, collapsing and Gromov–Hausdorff convergence, analysis and geometry on Alexandrov spaces, moduli spaces of Riemannian metrics, transformation groups, stochastic analysis on Riemannian manifolds, loop spaces and symplectic geometry, medical robotics, and mathematical epidemiology.

Research Collaborations

• HeKKSaGOn - Mathematics at the Interface of Science and Technology

• DFG-Graduiertenkolleg 2229 Asymptotische Invarianten und Limiten von Gruppen und Räumen

• DFG-Schwerpunktprogramm ‘Geometrie im Unendlichen’ (SPP 2026)

• Spaces and Moduli Spaces of Riemannian Metrics with Curvature Bounds on compact and non-compact Manifolds