2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/209461We 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. Our conjecture in Hurwitz theory follows from this recursion for the framed vertex in the limit of infinite framing.21 pages, 5 figures, small corrections, references addedAlgebraic GeometryHigh Energy Physics - Theory81T30; 57M27; 14N35text