The asymptotic viewpoint in geometry provides a common framework for discrete and continuous spaces and underlies our research program. The research program is structured into three core research areas:
 

A Asymptotic invariants of groups and spaces

• A1 Higher order Dehn functions
• A2 Boundaries
• A3 ℓ2-Invariants

B Deformation and moduli spaces

• B1 Geometric structures on infinite surfaces
• B2 Flows and parametrizations of deformation spaces
• B3 Moduli spaces of Riemannian metrics and the Willmore functional on moduli spaces of curves

C Converengence, limits and degenerations of spaces

• C1 Solutions of geometric partial differential equations
• C2 Compactifications
• C3 Invariant random subgroups and notions of convergence