JournalsjemsVol. 10 , No. 2DOI 10.4171/jems/115

Invariance of tautological equations I: conjectures and applications

  • Y.-P. Lee

    University of Utah, Salt Lake City, United States
Invariance of tautological equations I: conjectures and applications cover

Abstract

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.