@article {1991, title = {Differential geometry of moduli spaces and its applications to soliton equations and to topological conformal field theory}, year = {1991}, institution = {Scuola Normale Superiore di Pisa}, abstract = {We 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.}, url = {http://hdl.handle.net/1963/6475}, author = {Boris Dubrovin} }