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Quantum Teichmuller theory and conformal field theory

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Julien Roger (Rutgers)

Abstract:
The aim of this talk is to investigate the possible connection between the
quantum Teichmuller space and a certain type of conformal field theory. I
will first introduce the notion of a modular functor arising from
conformal field theory, and its applications to low dimensional topology.
Then I will describe the construction of the quantum Teichmuller space,
emphasizing the relationship with hyperbolic geometry. Finally, I will
describe a possible connection between the two constructions, focusing on
the notion of factorization rule. The key ingredients here are the
Deligne-Mumford compactification of the moduli space and its
Weil-Petersson geometry. I will introduce these notions as well.