Differential geometry and geometric analysis are well represented, with particular emphasis on symplectic geometry, gauge theories with applications to low-dimensional topology, harmonic mappings, minimal (and CMC) surfaces and geometric PDE.

Research interests in topology include: homotopy theory of spaces of smooth embeddings and diffeomorphisms, abstract homotopy theory, 3-manifold topology and combinatorial topology of surfaces. Connections with algebraic geometry include the study of algebraic cycles by methods derived from number theory and analysis, as well as Gromov-Witten theory.

Another strength lies in the area of discrete groups and geometric structures on low-dimensional manifolds. This includes hyperbolic manifolds, complex hyperbolic manifolds, Teichmüller theory and Kleinian groups, and the study of representations spaces of surface groups and 3-manifold groups into Lie groups.

There is an active postdoctoral group, and a weekly geometry and topology seminar, as well as a longer-format dynamics and geometry seminar that meets every other week.