We construct an integrable hierarchy in the form of Hirota quadratic equations (HQEs) that governs the Gromov–Witten invariants of the Fano orbifold projective curve . The vertex operators in our construction are given in terms of the –theory of via Iritani’s –class modification of the Chern character map. We also identify our HQEs with an appropriate Kac–Wakimoto hierarchy of ADE type. In particular, we obtain a generalization of the famous Toda conjecture about the GW invariants of to all Fano orbifold curves.
"Gromov–Witten theory of Fano orbifold curves, Gamma integral structures and ADE-Toda hierarchies." Geom. Topol. 20 (4) 2135 - 2218, 2016. https://doi.org/10.2140/gt.2016.20.2135