
The (Generalized) Kontsevich Matrix Model is known to be relevant for describing 2d topological minimal models coupled to gravity. We shall build a solution for this model in terms of resolvents (loop operator averages) starting from Virasoro constraints on partition function (i.e. Ward identities for the corresponding matrix integral). It turns out that resolvents can be considered as meromorphic multidifferentials on a certain auxiliary Riemann surface (complex spectral curve). Different phases of the theory correspond to different Riemann surfaces. We shall discuss various features of this construction, in particular, the socalled pq duality in terms of resolvents and corresponding Riemann surfaces in the example of dualities between (2,3) and (3,2) models.
