We prove two structure theorems for the Gromov-Witten theory of the quintic threefolds, which together give an effective algorithm for the all genus Gromov-Witten potential functions of quintics. By using these structure theorems, we prove Yamaguchi-Yau's Polynomial Ring Conjecture in this paper and prove Bershadsky-Cecotti-Ooguri-Vafa's Feynman rule conjecture in the subsequent paper.
Huai-Liang Chang. Shuai Guo. Jun Li. "Polynomial structure of Gromov–Witten potential of quintic 3-folds." Ann. of Math. (2) 194 (3) 585 - 645, November 2021. https://doi.org/10.4007/annals.2021.194.3.1