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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

An algebro-geometric proof of Witten's conjecture


Authors: M. E. Kazarian and S. K. Lando
Journal: J. Amer. Math. Soc. 20 (2007), 1079-1089
MSC (2000): Primary 14H70; Secondary 14H10
Published electronically: March 23, 2007
MathSciNet review: 2328716
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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.


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Additional Information

M. E. Kazarian
Affiliation: Steklov Institute of Mathematics, Russian Academy of Sciences, 8 Gubkina Street, Moscow, 117966 Russia, and The Poncelet Laboratory, Independent University of Moscow, 11, Bolshoy Vlasyevskiy Pereulok, Moscow, 121002 Russia
Email: kazarian@mccme.ru

S. K. Lando
Affiliation: Institute for System Research, Russian Academy of Sciences, Nakhimovskii pr., 36 korp. 1, Moscow, 117218 Russia, and The Poncelet Laboratory, Independent University of Moscow, 11, Bolshoy Vlasyevskiy Pereulok, Moscow, 121002 Russia
Email: lando@mccme.ru

DOI: http://dx.doi.org/10.1090/S0894-0347-07-00566-8
PII: S 0894-0347(07)00566-8
Keywords: Algebraic curves, moduli spaces, Witten conjecture, Hurwitz numbers, KP equation
Received by editor(s): August 5, 2005
Published electronically: March 23, 2007
Additional Notes: The first author was supported in part by the grants RFBR 04-01-00762, RFBR 05-01-01012-a, NWO-RFBR 047.011.2004.026 (RFBR 05-02-89000-NWOa), GIMP ANR-05-BLAN-0029-01.
The second author was supported in part by the grants ACI-NIM-2004-243 (Noeuds et tresses), RFBR 05-01-01012-a, NWO-RFBR 047.011.2004.026 (RFBR 05-02-89000-NWOa), GIMP ANR-05-BLAN-0029-01.
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.