Prof. Bernd Schroers

Boundary terms and symplectic structure in the Chern-Simons formulation of 2+1 dimensional gravity

In 2+1 dimensions Eintein's theory of gravity can be formulated as a gauge group with the Poincare group as the gauge group. In my talk I will explain how to introduce point particles and how to model universes with boundaries in the Chern-Simons formulation. I will also sketch how the (finite dimensional) phase space of the theory can be parametrised and how its symplectic structure can be computed. I will end with remarks about the quantisation of the theory, in particular the role played by quantum groups.