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Witten's conjecture, Virasoro conjecture, and invariance of tautological equations

Yuan-Pin Lee Department of Mathematics, University of Utah, Salt Lake City, Utah, 84112

Algebraic Geometry mathscidoc:2204.45024

2004.5
The main goal of this paper is to prove the following two conjectures for genus up to two: 1. Witten's conjecture on the relations between higher spin curves and Gelfand--Dickey hierarchy. 2. Virasoro conjecture for target manifolds with conformal semisimple Frobenius manifolds. The main technique used in the proof is the invariance of tautological equations under loop group action.
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@inproceedings{yuan-pin2004witten's,
  title={Witten's conjecture, Virasoro conjecture, and invariance of tautological equations},
  author={Yuan-Pin Lee},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220415114300618498042},
  year={2004},
}
Yuan-Pin Lee. Witten's conjecture, Virasoro conjecture, and invariance of tautological equations. 2004. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220415114300618498042.
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