R. Inanc Baykur, Tom Braden, Weimin Chen, Owen Gwilliam, Paul Hacking, Rob Kusner, Andrea Nahmod, Alexei Oblomkov, Franz Pedit, Martina Rovelli, Mike Sullivan. Postdocs: Jie Min, Jin-Cheng Guu.

Emeritus: William Meeks, Ivan Mirkovic.

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.

## Research Areas

**Differential geometry and analysis:** Weimin Chen, Rob Kusner, Andrea Nahmod, William Meeks, Franz Pedit, Mike Sullivan

**Low dimensional topology:** R. Inanc Baykur, Weimin Chen, Rob Kusner, William Meeks, Alexei Oblomkov

**Symplectic geometry and topology: **R. Inanc Baykur, Tom Braden, Weimin Chen, Paul Hacking, Mike Sullivan, Franz Pedit

**Homological algebra, Lie groups: **Tom Braden, Owen Gwilliam, Ivan Mirkovic, Alexei Oblomkov

**Higher category theory and Homotopy theory:** Owen Gwilliam, Martina Rovelli

## Department of Mathematics and Statistics