Abstract:

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.

(Link:https://projecteuclid.org/journals/annals-of-mathematics/volume-194/issue-3/Polynomial-structure-of-GromovWitten-potential-of-quintic-3-folds/10.4007/annals.2021.194.3.1.full)

Papers Published：
[1] Holomorphic anomaly equation for (P2,E) and the Nekrasov-Shatashvili limit of local P2,arXiv:2001.05347, with Pierrick Bousseau, Honglu Fan and Longting Wu. Forum of Mathematics, Pi (2021), Vol.9, e3, 1–57.
[2] The theory of N-Mixed-Spin-P fields, arXiv: 1809.08806, to appear in Geometry & Topology, with Huai-Liang Chang, Jun Li and Wei-Ping Li. Geometry & Topology 25 (2021) 775–811.
[3] The Genus-One Global Mirror Theorem for the Quintic Threefold, arXiv:1703.06955, Compositio Mathematica, Vol. 155, Issue 5, 995-1024, (2019), with Dustin Ross.
[4] Genus-One Mirror Symmetry in the Landau-Ginzburg Model, arXiv:1611.08876, Algebraic Geometry, Vol. 6, Issue 3, 260-301, (2019), with Dustin Ross.

         Prof. Guo Shuai