Resumen de Invariance of tautological equations I: conjectures and applications
The main goal of this paper is to introduce a set of conjectures on the relations in the tautological rings. In particular, this framework gives an efficient algorithm to calculate all tautological equations using only finite dimensional linear algebra. Other applications include the proofs of \emph{Witten's conjecture} on the relations between higher spin curves and Gelfand--Dickey hierarchy and \emph{Virasoro conjecture} for target manifolds with conformal semisimple quantum cohomology, both for genus up to two.
