Tau-function on Hurwitz spaces and spaces of holomorphic differentials on Riemann surfaces and new relations in Picard group of these spaces.

The goal of the talk is to show how structures from the theory of integrable systems can be applied to study geometry of various moduli spaces: spaces of admissible covers and spaces of abelian and quadratic differentials on Riemann surfaces. The central object is the so-called Jimbo-Miwa tau-function corresponding to isomonodromic deformations of linear systems of differential equations with meromorphic coefficients. The talk is based on joint works with A.Kokotov and P.Zograf.