Descendent Tropical Mirror Symmetry for $\mathbb{P}^2$

Abstract

We modify Gross's construction of mirror symmetry for $\mathbb{P}^2$ by introducing a descendent tropical Landau-Ginzburg potential. The period integrals of this potential compute a modification of Givental's J-function, explicitly encoding a larger sector of the big phase space. As a byproduct of this construction, new tropical methods for computing certain descendent Gromov-Witten invariants are defined.