| WDVV equations were discovered by physicists Witten, Dijkgraaf, E.Verlinde and H.Verlinde in the beginning of `90s. Any solution (primary free energy) of WDVV describes moduli space of topological field theory. Dubrovin invented Frobenius manifold as the coordinate-free form of WDVV equation. For massive Frobenius manifolds (semi-simple), they can be descirbed by Darboux-Egoroff system. Given any solution of WDVV equation, we can construct the hierarchy structure (Hamiltonian system of Hydrodynamic type) associated with the solution. In physics language, this hierarchy will correspond to the Witten's topological recursion relation in coupling topological gravity. We can construct the quasi-classical tau-function (genus zero) of the WDVV hierarchy such that it's the extension of the solution (primary free energy). Also, for massive Frobenius manifold the hierarchy can be diagonalized by the so-called canonical coordinate (Whitham equations). In this talk, we will study these constructions, such as canonical coordinate, Darboux-Egoroff system, WDVV hierarchy, quasi-classical tau-function. We also discuss the basic examples of massive Frobenius manifold-Hurwitz spaces. Finally, we can talk about some open problems in this area. |