Bulk-Deformed Potentials for Toric Fano Surfaces, Wall-Crossing, and Period

 We provide an inductive algorithm to compute the bulk-deformed potentials for toric Fano surfaces via wall-crossing techniques and a tropical–holomorphic correspondence theorem for holomorphic discs. As an application of the correspondence theorem, we also prove a big quantum period theorem for toric Fano surfaces, which relates the log descendant Gromov–Witten invariants with the oscillatory integrals of the bulk-deformed potentials.