Speaker: Xiaobo Liu, Columbia University
Title of talk: Quantum hyperbolic invariants of surface diffeomorphisms
Abstract: We considerthe Quantum Teichmuller Space of the punctured surface introduced by Chekhov-Fock-Kashaev,and formalize it as a noncommutative deformation of the space of the algebraicfunctions on the Teichmuller space of the surface. We then investigate therepresentation theory of this algebraic object and define a quantum hyperbolic invariant forpseudo-Anosov diffeomorphisms of the surface. We compute this invariant in thecase of the 1-puncture torus and and the 4-puncture
sphere.