An algebro-geometric proof of Witten's conjecture

Abstract

We present a new proof of Witten's conjecture. The proof is based on the analysis of the relationship between intersection indices on moduli spaces of complex curves and Hurwitz numbers enumerating ramified coverings of the 2-sphere.

12 pages, no figures

References in corpus (7)

• Hurwitz numbers and intersections on moduli spaces of curves
• Gromov-Witten theory, Hurwitz numbers, and Matrix models, I
• On Hurwitz numbers and Hodge integrals
• Geometry of meromorphic functions and intersections on moduli spaces of curves
• Hodge integrals and Hurwitz numbers via virtual localization
• The Toda equations and the Gromov-Witten theory of the Riemann sphere
• Enumeration of ramified coverings of the sphere and 2-dimensional gravity

Cited by in corpus (63)

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• The moduli space of curves, double Hurwitz numbers, and Faber's intersection number conjecture
• Monotone Hurwitz numbers and the HCIZ integral II
• Toda Equations and Piecewise Polynomiality for Mixed Double Hurwitz Numbers
• On the Complex Asymptotics of the HCIZ and BGW Integrals
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• Generalized string equations for double Hurwitz numbers
• Intersection numbers with Witten's top Chern class
• The hypergeometric functions of the Faber-Zagier and Pixton relations
• JT gravity and the asymptotic Weil-Petersson volume
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• Towards large genus asymtotics of intersection numbers on moduli spaces of curves
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• Localization, Hurwitz Numbers and the Witten Conjecture
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• Polynomiality of monotone Hurwitz numbers in higher genera
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