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Geometry & Topology

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 R3 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 Cheninfo-icon, Rob Kusnerinfo-icon, Andrea Nahmodinfo-icon, William Meeksinfo-icon, Franz Peditinfo-icon, Mike Sullivaninfo-icon

Low dimensional topology: R. Inanc Baykurinfo-icon, Weimin Cheninfo-icon, Rob Kusnerinfo-icon, William Meeksinfo-icon, Alexei Oblomkovinfo-icon

Symplectic geometry and topology: R. Inanc Baykurinfo-icon, Tom Bradeninfo-icon, Weimin Cheninfo-icon, Paul Hackinginfo-icon, Mike Sullivaninfo-icon, Franz Peditinfo-icon

Homological algebra, Lie groups: Tom Bradeninfo-icon, Owen Gwilliaminfo-icon, Ivan Mirkovicinfo-icon, Alexei Oblomkovinfo-icon

Higher category theory and Homotopy theory: Owen Gwilliaminfo-icon, Martina Rovelliinfo-icon