Research Summary
My research is at the interface of algebra, geometry, topology and mathematical physics.
Keywords
- (quantum) topology: topological quantum field theories, manifold invariants, state sum models, defects in topological quantum field theories and in topological quantum computing, mapping class groups
- algebra: (braided) monoidal categories, tensor categories, fusion categories, module categories, higher categories, representation theory of Hopf algebras, diagrammatic calculi
- geometry: Poisson-Lie groups, Poisson homogeneous spaces, classical (dynamical) r-matrices, moduli spaces of flat bundles on oriented surfaces, aspects of Teichmüller theory, aspects of constant curvature Lorentzian geometry in 3d, aspects of hyperbolic geometry
- mathematical physics: Chern-Simons theory, models in topological quantum computing (e.g. quantum double models), 3d gravity
More information about my research can be found on the following pages