Julien Roger, USC

TITLE: Quantum Teichmuller spaces and modular functors

ABSTRACT: Let S be a surface with punctures. The quantum Teichmuller space T^q(S) is a deformation of the algebra of rational functions on the classical Teichmuller space T(S). Bonahon and Liu obtained a classification of the representations of T^q(S). Using this classification one can construct a vector bundle over the moduli space M(S). I will describe the first steps in trying to extend this construction to the Deligne-Mumford compactification of M(S). It involves looking at families of hyperbolic metrics where the length of a finite number of geodesics tends to 0, and the way this affects ideal triangulations on S. I will also explain how it relates to the notion of a modular functor.