Tau functions and cohomology of moduli spaces

In the theory of integrable systems tau functions are canonical generators of commuting flows and appear naturally in the study of isomonodromic deformations of differential equations, Frobenius structures, etc. Tau functions often have algebro-geometric significance and can be interpreted as sections of holomorphic line bundles on moduli spaces. We will explain how to compute the divisors of tau functions and to obtain non-trivial relations in the Picard groups of the moduli spaces of meromorphic functions, as well as those of abelian and quadratic differentials, on complex algebraic curves.
The talk will be held in Russian.