The Eynard-Orantin recursion and equivariant mirror symmetry for the   projective line
  We study the equivariantly perturbed mirror Landau-Ginzburg model of the projective line. We show that the Eynard-Orantin recursion on this model encodes all genus all descendants equivariant Gromov-Witten invariants of the projective line. The non-equivariant limit of this result is the Norbury-Scott conjecture, while by taking large radius limit we recover the Bouchard-Marino conjecture on simple Hurwitz numbers. 
Bohan Fang, Chiu-Chu Melissa Liu, Zhengyu Zong
math.AG