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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, guage 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.

**PARTICIPATING FACULTY**

Tarik Aougab, Tamarkin Assistant Professor of Mathematics

Thomas Banchoff, Professor Emeritus of Mathematics

George Daskalopoulos, Professor of Mathematics

Tom Goodwillie, Professor of Mathematics

Bruno Harris, Professor Emeritus of Mathematics

Jeremy Kahn, Professor of Mathematics

Nicos Kapouleas, Professor of Mathematics

Richard Kenyon, William R. Kenan, Jr. University Professor

Wai Yeung Lam, Tamarkin Assistant Professor of Mathematics

Kathryn Mann, Assistant Professor of Mathematics

Richard Schwartz, Professor of Mathematics

**SEMINARS**