Topology, Geometry and Mathematical Physics

Geometry and topology are core areas of mathematics that have recently experienced rapid development, leading to the solution of the century-old Poincaré conjecture and providing key ideas that underlie general relativity, string theory and high-energy physics.

What these branches of mathematics have in common is their concern with the fundamental notion of shape. NC State’s geometers and topologists draw on tools from many other areas of mathematics — algebra, analysis, combinatorics, differential equations and representation theory — to answer questions about the nature of shape. Research directions of particular interest include low-dimensional topology and knot theory, symplectic geometry and topology, homotopy theory and geometric flows.

Geometry and topology have also emerged as rich sources of methods and ideas for solving problems in other fields of mathematics as well as in contemporary science and engineering, Members of our group are using their expertise to answer questions ranging from how to teach a computer to recognize images to determining the shape of the universe.

Bojko Bakalov


Mathematical physics, Lie algebras, vertex algebras, integrable systems.

Patricia Hersh

Adjunct Professor

Algebraic and topological combinatorics.

Naihuan Jing


Representation theory, quantum groups, infinite-dimensional Lie algebras and groups, vertex algebras, algebraic combinatorics, quantum computation.

Corey Jones

Assistant Professor

Tensor categories, mathematical physics, operator algebras, higher categories.


Arkady Kheyfets


Mathematical physics; classical and quantum gravity, quantum cosmology, gauge theories, general relativity.

Irina Kogan


Geometric study of differential equations and variational problems; equivalence and symmetry problems; computational invariant theory.


Thomas Lada

Professor Emeritus

Algebraic topology, homotopy theory, cohomology operations.

Tye Lidman

Assistant Professor

Topology, Geometry.

Peter McGrath

Assistant Professor

Geometric Analysis, Minimal Surfaces, Partial Differential Equations

Larry Norris

Associate Professor Emeritus

Mathematical physics; general relativity, gauge theories, unified field theories; generalized symplectic geometry.

Teemu Saksala

Assistant Professor

Geometric inverse problems related to seismology.

Radmila Sazdanovic

Assistant Professor