The main goal of this paper is to introduce a set of conjectures on the relations in the tautological rings. In particular, the framework gives an efficient algorithm to calculate all tautological equations using only finite dimensional linear algebra. Other applications are also indicated.
In this paper, we extend our previous work to construct (0, 2) Toda-like
mirrors to A/2-twisted theories on more general spaces, as part of a program of understanding (0,2) mirror symmetry. Specifically, we propose (0, 2)
mirrors to GLSMs on toric del Pezzo surfaces and Hirzebruch surfaces with
deformations of the tangent bundle. We check the results by comparing correlation functions, global symmetries, as well as geometric blowdowns with the
corresponding (0, 2) Toda-like mirrors. We also briefly discuss Grassmannian