We explain how to construct a quantum deformation of a spectral curve to a tau-function of the KP hierarchy. This construction is applied to Witten-Kontsevich tau-function to give a natural explanation of some earlier work. We also apply it to higher Weil-Petersson volumes and Witten's r-spin intersection numbers.
Emergent Geometry of KP Hierarchy. II
On an algebro-geometric discretization of KP hierarchy
hbar-expansion of KP hierarchy: Recursive construction of solutions
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