Riemann-Hilbert problems on Hurwitz-Frobenius manifolds

There are two (dual) Riemann-Hilbert problems naturally associated to every Frobenius manifold. In this talk I will present solutions to the Riemann-Hilbert problems corresponding to Frobenius structures on Hurwitz spaces (moduli spaces of functions over Riemann surfaces). The solutions are given in terms of meromorphic bidifferentials defined on the underlying surface. In the case of Hurwitz spaces corresponding to hyperelliptic coverings the Stokes matrix and monodromy matrices are computed.