We construct a sheaf of Fock spaces over the moduli space of elliptic curves with -level structure, arising from geometric quantization of , and a global section of this Fock sheaf. The global section coincides, near appropriate limit points, with the Gromov–Witten potentials of local and of the orbifold . This proves that the Gromov–Witten potentials of local are quasimodular functions for the group , as predicted by Aganagic, Bouchard, and Klemm, and it proves the crepant resolution conjecture for in all genera.
"Gromov–Witten invariants of local and modular forms." Kyoto J. Math. 61 (3) 543 - 706, September 2021. https://doi.org/10.1215/21562261-2021-0010