Weighted Hurwitz numbers and topological recursion

The KP and 2D Toda tau-functions of hypergeometric type that serve as generating functions for weighted single and double Hurwitz numbers are related to the topological recursion programme. A graphical representation of such weighted Hurwitz numbers is given in terms of weighted constellations. The associated classical and quantum spectral spectral curves are derived. The pair correlators are given a finite Christoffel-Darboux representation. The WKB series for the Baker function is derived and used to deduce the loop equations and the topological recursion relations. This is a joint work with G. Chapuy, B. Eynard, and J. Harnad