Hurwitz numbers, matrix models and enumerative geometry

  title={Hurwitz numbers, matrix models and enumerative geometry},
  author={Vincent Bouchard and Marcos Mari{\~n}o},
  journal={arXiv: Algebraic Geometry},
We propose a new, conjectural recursion solution for Hurwitz numbers at all genera. This conjecture is based on recent progress in solving type B topological string theory on the mirrors of toric Calabi-Yau manifolds, which we briefly review to provide some background for our conjecture. We show in particular how this B-model solution, combined with mirror symmetry for the one-leg, framed topological vertex, leads to a recursion relation for Hodge integrals with three Hodge class insertions… 

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