Other Author affiliation: Imperial College London/CNRS Unreviewed Non UBC I will present work in progress suggesting a conjecturally general correspondence relating quantum (Chern-Simons) invariants of knots in three-space to (Eynard-Orantin) higher genus mirror symmetry, the computation of the former being solved by the latter. The correspondence rests on the identification of a natural group of piecewise linear transformations on both sides of the correspondence.