{
  "id": "1202.1159",
  "version": "v1",
  "published": "2012-02-06T14:57:44.000Z",
  "updated": "2012-02-06T14:57:44.000Z",
  "title": "The spectral curve of the Eynard-Orantin recursion via the Laplace transform",
  "authors": [
    "Olivia Dumitrescu",
    "Motohico Mulase",
    "Brad Safnuk",
    "Adam Sorkin"
  ],
  "comment": "49 pages, 7 figures",
  "categories": [
    "math.AG",
    "math-ph",
    "math.CO",
    "math.MP"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-02-06T14:57:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H15",
      "14N35",
      "05C30",
      "11P21",
      "81T30"
    ],
    "keywords": [
      "spectral curve",
      "laplace transform",
      "recursion kernel",
      "eynard-orantin recursion formula",
      "stationary gromov-witten invariants"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 49,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1340771,
      "adsabs": "2012arXiv1202.1159D"
    }
  }
}