An algebro-geometric proof of Witten's conjecture

By M. Kazarian, Sergei K. Lando. 2006

171 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/d65eb061fcc9ac664243f8a533171c147670f55d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. M. Mulase
2. Naizhen Zhang
3. Dimitri Zvonkine
4. Sergey Shadrin
5. L. Spitz
6. A. Mironov
7. A. Morozov
8. Hsian-Hua Tseng

In Discrete Mathematics and Combinatorics

1. M. Mulase
2. Naizhen Zhang
3. Sergey Shadrin
4. A. Mironov
5. L. Spitz
6. A. Morozov
7. Hsian-Hua Tseng
8. Pilar Johnson

In Geometry and Topology

1. Dimitri Zvonkine
2. M. Mulase
3. L. Spitz
4. Naizhen Zhang
5. Sergey Shadrin
6. R. Pandharipande
7. A. Morozov
8. A. Mironov

Citations in the corpus

• LOCALIZATION IN GROMOV-WITTEN THEORY AND ORBIFOLD GROMOV-WITTEN THEORY (2011, unknown): “By now, Witten’s conjecture has been reproved many times (Okounkov-Pandharipande [48], Mirzakhani [45], Kim-Liu [35], Kazarian-Lando [34], Chen-Li-Liu [10], Kazarian [33], Mulase-Zhang [46], etc.”
• Algebra of differential operators associated with Young diagrams (2012, background): “ramewroks: strings and QCD [8], mirror symmetry [7], theory of singularities [1], matrix models [16, 20], integrable systems [26, 14, 25], Yang-Mills theory [6, 14] and the theory of moduli of curves [13, 12, 20] and other branches of string theory. 9 Associate with Young diagrams ∆1,...,∆k and ∆, w”
• Polynomiality of monotone Hurwitz numbers in higher genera (2012, unknown): “[13] M. E. Kazarian and S. K. Lando, An algebro-geometric proof of Witten’s conjecture, J. Amer.”
• Abelian Hurwitz-Hodge integrals (2008, methodology): “The first is the determination of descendent integra ls overMg,n via asymptotics to remove the Hodge classes [18, 21].”
• Equivalence of ELSV and Bouchard–Mariño conjectures for $$r$$r-spin Hurwitz numbers (2013, background): “The proof of this theorem is a straightforward generalization of [24] and [30].”
• Polynomial recursion formula for linear Hodge integrals (2009, background): “Denote by πg,ℓ : Mg,ℓ+1 → Mg,ℓ the natural projection and by ωπg,ℓ the relative dualizing sheaf of the universal curve πg,ℓ.”