The spectral curve of the Eynard-Orantin recursion via the Laplace   transform
  The Eynard-Orantin recursion formula provides an effective tool for certain enumeration problems in geometry. The formula requires a spectral curve and the recursion kernel. We present a uniform construction of the spectral curve and the recursion kernel from the unstable geometries of the original counting problem. We examine this construction using four concrete examples: Grothendieck's dessins d'enfants (or higher-genus analogue of the Catalan numbers), the intersection numbers of tautological cotangent classes on the moduli stack of stable pointed curves, single Hurwitz numbers, and the stationary Gromov-Witten invariants of the complex projective line. 
Olivia Dumitrescu, Motohico Mulase, Brad Safnuk, and Adam Sorkin
math.AG math-ph math.CO math.MP