Research
Research Summary
My research interests are at the interface of algebra, geometry, topology and mathematical physics. See the following keywords.
topology
- topological quantum field theories
- topological quantum field theories with defects
- state sum models of topological quantum field theories and manifold invariants
- quantum invariants of knots and 3-manifolds
- mapping class groups
- state sum models in topological quantum computing
algebra
- monoidal and braided monoidal categories
- tensor categories, fusion categories, module categories
- higher categories
- representation theory of Hopf algebras and quantum groups
geometry
- Poisson-Lie groups, Poisson homogeneous spaces
- classical r-matrices and dynamical classical r-matrices
- contractions and deformations of Poisson-Lie groups
- moduli spaces of flat bundles on oriented surfaces, representation varieties
- aspects of Teichmüller theory: Fuchsian groups, grafting and earthquakes,…
- aspects of constant curvature Lorentzian and hyperbolic geometry in 3d
mathematical physics
- quantum geometry
- Chern-Simons theory
- 3d gravity