Publication

Combinatorics of Loop Equations for Branched Covers of Sphere

Nicolas Gerson Orantin
2018
Journal Articles

Abstract

We prove, in a purely combinatorial way, the spectral curve topological recursion for the problem of enumeration of bi-colored maps, which are dual objects to dessins d'enfant. Furthermore, we give a proof of the quantum spectral curve equation for this problem. Then we consider the generalized case of four-colored maps and outline the idea of the proof of the corresponding spectral curve topological recursion.

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Combinatorics of Loop Equations for Branched Covers of Sphere

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