The faculty at UMass Amherst and the surrounding colleges have broad interests in geometry and topology that include knot theory (topological and geometric knot invariants), symplectic geometry (holomorphic curves applied to rigidity and dynamics), low-dimensional topology (smooth structures on 4-manifolds, geometric structures on 3-manifolds), orbifold theory (manifolds with local group actions, orbifold Gromov-Witten invariants), string topology (algebraic structures on loop spaces), higher categories (foundational aspects, and applications to physics and geometry), factorization algebras and operads, surfaces given by variational problems (harmonic, minimal, constant mean curvature, Willmore surfaces, in **R**^{3} and other target spaces), variational and evolution problems (for harmonic maps, Yamabe metrics, etc.), integrable systems (a tool for studying special surfaces, harmonic maps, etc.), harmonic analysis (to obtain PDE estimates, especially applied to dispersive and hyperbolic analogues of harmonic maps) and mathematical visualization.

The faculty (and others) also participate in the Geometry and Topology Seminar, the Joint Math/Physics Seminar and the Valley Geometry Seminar.

## Faculty

Professor; Director, Graduate Program

Associate Professor

Professor

Professor

Professor

Assistant Professor

## Postdocs

## Emeritus

Professor Emeritus

##
Research Areas

### Differential geometry and analysis

Professor

Professor

### Low dimensional topology

Professor

Professor

### Symplectic geometry and topology

Professor; Director, Graduate Program

### Homological algebra, Lie groups

Professor; Director, Graduate Program

Associate Professor

Professor Emeritus

Professor

### Higher category theory and Homotopy theory

Associate Professor

Assistant Professor

## Related Faculty at the Five Colleges

Amherst College

Mount Holyoke College

Smith College