Research

Reseach Summary

My research interests are at the interface of algebra and mathematical physics. More specifically, I am interested in mathematical structures arising in three-dimensional gravity, Chern-Simons theory and quantum geometry. These interest of these research subjects is that they tie together a variety of topics from algebra, geometry and topology:

Algebra

• Poisson-Lie groups
• Hopf algebras and quantum groups
• representation theory of Lie groups and quantum groups
• (braided) monoidal categories and higher categories
• braid groups and mapping class groups
• Fuchsian groups

Geometry

• Moduli spaces of flat connections
• Poisson and symplectic geometry
• Teichmüller theory
• differential geometry in three dimensions
• hyperbolic geometry in two and three dimensions

Topology

• link and knot invariants
• quantum invariants of manifolds contructed from representation theory
• topological quantum field theories