Geodesic
Invariance of tautological equations I: conjectures and applications
Journal of the European Mathematical Society, Tome 10 (2008) no. 2, pp. 399-413.

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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 Witten's conjecture on the relations between higher spin curves and Gelfand–Dickey hierarchy and Virasoro conjecture for target manifolds with conformal semisimple quantum cohomology, both for genus up to two.
DOI : 10.4171/jems/115
Classification : 14-XX, 00-XX
Keywords: Moduli of curves, tautological rings, Gromov-Witten theory 
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     title = {Invariance of tautological equations {I:} conjectures and applications},
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Y.-P. Lee. Invariance of tautological equations I: conjectures and applications. Journal of the European Mathematical Society, Tome 10 (2008) no. 2, pp. 399-413. doi : 10.4171/jems/115. http://geodesic.mathdoc.fr/articles/10.4171/jems/115/

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