In the Givental's theory, the quantum cohomology ring is obtained as the
classical limit of the quantum differential equation for the J-function.
As the reverse problem, I would like to discuss a reconstruction of the
quantum differential equation and the J-function from the quantum
cohomology ring via the topological recursion. In particular for the case
of the projective space and the Fano complete intersection of
hypersurfaces of the degree 1, it is shown that the quantum differential
equation is reconstructible as the quantum curve for the spectral curve
referred to the GKZ curve. In this talk, I would like to overview the
reconstruct of the quantum curve via the topological recursion, and
explain how such a reconstruction is applied to the quantum differential
equation and J-function. This talk is based on the work collaborated with
K. Iwaki, M. Manabe, and I. Satake.
Reference: H. Fuji, K. Iwaki, M. Manabe, and I. Satake,
“Reconstructing GKZ via topological recursion,” arXiv:1708.09365[math-ph].