Group in Geometry and Topology at Brown University
The faculty in geometry and topology at Brown represent a broad set of strengths, from homotopy theory, to low-dimensional topology, to geometric analysis and symplectic geometry.
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.
Thomas Banchoff, Professor Emeritus of Mathematics
Jeffrey Brock, Associate Professor of Mathematics
George Daskalopoulos, Professor of Mathematics
Tom Goodwillie, Professor of Mathematics
Bruno Harris, Professor Emeritus of Mathematics
Nicos Kapouleas, Professor of Mathematics
Richard Kenyon, William R. Kenan, Jr. University Professor
Sara Maloni, Tamarkin Professor of Mathematics
Richard Schwartz, Professor of Mathematics