Quantum group structure for moduli space M1,1

In this talk we present a possibility to quantize moduli spaces of algebraic curves. We restrict ourselves to the simplest case of a modular space anti M1,1 - a torus with one puncture. We consider an explicit coordinatization of this space in the Kontsevich picture, where integrals of the first Chern classes may be done over moduli (orbi-)spaces generating intersection indices (correlation functions for the model of topological gravity). The Kontsevich matrix model (KMM) provides a generating function for the intersection indices. (orig.)