01022nas a2200109 4500008004100000245012700041210006900168260003700237520058200274100002000856856003600876 1991 en d00aDifferential geometry of moduli spaces and its applications to soliton equations and to topological conformal field theory0 aDifferential geometry of moduli spaces and its applications to s bScuola Normale Superiore di Pisa3 aWe construct flat Riemannian metrics on moduli spaces of algebraic curves with marked meromorphic function. This gives a new class of exact algebraic-geometry solutions to certain non-linear equations in terms of functions on the moduli spaces. We show that the Riemannian metrics on the moduli spaces coincide with two-point correlators in topological conformal field theory and calculate the partition function for A_n model for arbitrary genus. A universal method for constructing complete families of conservation laws for Whitham-type hierarchies of PDEs is also proposed.1 aDubrovin, Boris uhttp://hdl.handle.net/1963/6475