Combinatorial quantization of (Super) Chern-Simons gravity

In the Chern-Simons formulation of (Super)gravity in 3 dimensions, the phase space corresponds to the moduli space of (Super)flat G-connections, where G is (Super)Lie group which depends on the signature of space-time and the cosmological constant. In the talk we will see how the canonical Poisson structure of this moduli space is given in terms of a classical (Super) r-matrix and discuss how quantum (Super) R-matrices provide its quantisation (e.g. the quantum double D(SU(2)) quantises Euclidean 3d gravity). (This talk is based on joint work with Bernd Schroers).