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.

Faculty

Professor

A headshot of R. Inanc Baykur.
Research Interests: Geometry and Topology
A headshot of R. Inanc Baykur.

Professor; Director, Graduate Program

A headshot of Tom Braden.
Research Interests: Topology of algebraic varieties; Representation Theory; Combinatorics
A headshot of Tom Braden.

Professor

UMass collegiate M maroon on gray
Research Interests: Differential Geometry and Topology
UMass collegiate M maroon on gray

Associate Professor

A headshot of Owen Gwilliam.
Research Interests: quantum field theory, derived geometry, higher categories
A headshot of Owen Gwilliam.

Professor

UMass collegiate M maroon on gray
Research Interests: Algebraic geometry
UMass collegiate M maroon on gray

Professor

A headshot of Rob Kusner.
Research Interests: Geometric analysis and variational problems, low dimensional geometry & topology, mathematical visualization
A headshot of Rob Kusner.

Professor

Andrea Nahmod.
Research Interests: Harmonic and nonlinear Fourier Analysis; Partial Differential Equations.
Andrea Nahmod.

Professor

A headshot of Alexei Oblomkov.
Research Interests: Representation Theory, Algebraic Geometry and Mathematical Physics
A headshot of Alexei Oblomkov.

Professor

Franz Pedit
Research Interests: Differential geometry
Franz Pedit

Assistant Professor

Martina Rovelli.
Research Interests: Higher category theory, homotopy theory, algebraic topology
Martina Rovelli.

Professor

Mike Sullivan.
Research Interests: Symplectic Geometry & Topology
Mike Sullivan.

Postdocs

Visiting Assistant Professor

UMass collegiate M maroon on gray
Research Interests: Symplectic geometry
UMass collegiate M maroon on gray

Visiting Assistant Professor

UMass collegiate M maroon on gray
UMass collegiate M maroon on gray

Emeritus

Professor Emeritus

William Meeks.
Research Interests: Differential geometry
William Meeks.

Professor Emeritus

UMass collegiate M maroon on gray
Research Interests: Representation theory, algebraic geometry, Geometric Representation Theory, Quantum Field Theory, Number Theory, Algebraic Geometry
UMass collegiate M maroon on gray

Research Areas

Differential geometry and analysis

Professor

UMass collegiate M maroon on gray
Research Interests: Differential Geometry and Topology
UMass collegiate M maroon on gray

Professor

A headshot of Rob Kusner.
Research Interests: Geometric analysis and variational problems, low dimensional geometry & topology, mathematical visualization
A headshot of Rob Kusner.

Professor

Andrea Nahmod.
Research Interests: Harmonic and nonlinear Fourier Analysis; Partial Differential Equations.
Andrea Nahmod.

Professor Emeritus

William Meeks.
Research Interests: Differential geometry
William Meeks.

Professor

Franz Pedit
Research Interests: Differential geometry
Franz Pedit

Professor

Mike Sullivan.
Research Interests: Symplectic Geometry & Topology
Mike Sullivan.

Low dimensional topology

Professor

A headshot of R. Inanc Baykur.
Research Interests: Geometry and Topology
A headshot of R. Inanc Baykur.

Professor

UMass collegiate M maroon on gray
Research Interests: Differential Geometry and Topology
UMass collegiate M maroon on gray

Professor

A headshot of Rob Kusner.
Research Interests: Geometric analysis and variational problems, low dimensional geometry & topology, mathematical visualization
A headshot of Rob Kusner.

Professor Emeritus

William Meeks.
Research Interests: Differential geometry
William Meeks.

Professor

A headshot of Alexei Oblomkov.
Research Interests: Representation Theory, Algebraic Geometry and Mathematical Physics
A headshot of Alexei Oblomkov.

Symplectic geometry and topology

Professor

A headshot of R. Inanc Baykur.
Research Interests: Geometry and Topology
A headshot of R. Inanc Baykur.

Professor; Director, Graduate Program

A headshot of Tom Braden.
Research Interests: Topology of algebraic varieties; Representation Theory; Combinatorics
A headshot of Tom Braden.

Professor

UMass collegiate M maroon on gray
Research Interests: Differential Geometry and Topology
UMass collegiate M maroon on gray

Professor

UMass collegiate M maroon on gray
Research Interests: Algebraic geometry
UMass collegiate M maroon on gray

Professor

Mike Sullivan.
Research Interests: Symplectic Geometry & Topology
Mike Sullivan.

Professor

Franz Pedit
Research Interests: Differential geometry
Franz Pedit

Homological algebra, Lie groups

Professor; Director, Graduate Program

A headshot of Tom Braden.
Research Interests: Topology of algebraic varieties; Representation Theory; Combinatorics
A headshot of Tom Braden.

Associate Professor

A headshot of Owen Gwilliam.
Research Interests: quantum field theory, derived geometry, higher categories
A headshot of Owen Gwilliam.

Professor Emeritus

UMass collegiate M maroon on gray
Research Interests: Representation theory, algebraic geometry, Geometric Representation Theory, Quantum Field Theory, Number Theory, Algebraic Geometry
UMass collegiate M maroon on gray

Professor

A headshot of Alexei Oblomkov.
Research Interests: Representation Theory, Algebraic Geometry and Mathematical Physics
A headshot of Alexei Oblomkov.

Higher category theory and Homotopy theory

Associate Professor

A headshot of Owen Gwilliam.
Research Interests: quantum field theory, derived geometry, higher categories
A headshot of Owen Gwilliam.

Assistant Professor

Martina Rovelli.
Research Interests: Higher category theory, homotopy theory, algebraic topology
Martina Rovelli.