Results 1  10
of
68
On a proof of a conjecture of MarinoVafa on Hodge integrals
"... Abstract. We prove a remarkable formula for Hodge integrals conjectured by Mariño and Vafa [23] based on large N duality, using functorial virtual localization on certain moduli spaces of relative stable morphisms. 1. ..."
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Abstract. We prove a remarkable formula for Hodge integrals conjectured by Mariño and Vafa [23] based on large N duality, using functorial virtual localization on certain moduli spaces of relative stable morphisms. 1.
The Laplace transform of the cutandjoin equation and the BouchardMarino conjecture on Hurwitz numbers
"... Abstract. We calculate the Laplace transform of the cutandjoin equation of Goulden, Jackson and Vakil. The result is a polynomial equation that has the topological structure identical to the Mirzakhani recursion formula for the WeilPetersson volume of the moduli space of bordered hyperbolic surfa ..."
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Cited by 44 (16 self)
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Abstract. We calculate the Laplace transform of the cutandjoin equation of Goulden, Jackson and Vakil. The result is a polynomial equation that has the topological structure identical to the Mirzakhani recursion formula for the WeilPetersson volume of the moduli space of bordered hyperbolic surfaces. We find that the direct image of this Laplace transformed equation via the inverse of the Lambert Wfunction is the topological recursion formula for Hurwitz numbers conjectured by Bouchard and Mariño using topological string theory. Contents
A formula of twopartition Hodge integrals
"... Let Mg,n denote the DeligneMumford moduli stack of stable curves of genus g with n marked points. Let π: Mg,n+1 → Mg,n be the universal curve, and let ωπ be the relative dualizing sheaf. The Hodge bundle E = π∗ωπ ..."
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Cited by 36 (19 self)
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Let Mg,n denote the DeligneMumford moduli stack of stable curves of genus g with n marked points. Let π: Mg,n+1 → Mg,n be the universal curve, and let ωπ be the relative dualizing sheaf. The Hodge bundle E = π∗ωπ
A mathematical theory of the topological vertex
"... Abstract. We have developed a mathematical theory of the topological vertex— a theory that was originally proposed by M. Aganagic, A. Klemm, M. Mariño, and C. Vafa on effectively computing GromovWitten invariants of smooth toric CalabiYau threefolds derived from duality between open string theory ..."
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Cited by 36 (19 self)
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Abstract. We have developed a mathematical theory of the topological vertex— a theory that was originally proposed by M. Aganagic, A. Klemm, M. Mariño, and C. Vafa on effectively computing GromovWitten invariants of smooth toric CalabiYau threefolds derived from duality between open string theory of smooth CalabiYau threefolds and ChernSimons theory on three manifolds. 1.
The tropical vertex
"... Abstract. Elements of the tropical vertex group are formal families of symplectomorphisms of the 2dimensional algebraic torus. We prove ordered product factorizations in the tropical vertex group are equivalent to calculations of certain genus 0 relative GromovWitten invariants of toric surfaces. ..."
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Cited by 34 (11 self)
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Abstract. Elements of the tropical vertex group are formal families of symplectomorphisms of the 2dimensional algebraic torus. We prove ordered product factorizations in the tropical vertex group are equivalent to calculations of certain genus 0 relative GromovWitten invariants of toric surfaces. The relative invariants which arise have full tangency to a toric divisor at a single unspecified point. The method uses scattering diagrams, tropical curve counts, degeneration formulas, and exact multiple cover calculations in orbifold GromovWitten theory. Contents
The moduli space of curves and GromovWitten theory
, 2006
"... The goal of this article is to motivate and describe how GromovWitten theory can and has provided tools to understand the moduli space of curves. For example, ideas and methods from GromovWitten theory have led to both conjectures and theorems showing that the tautological part of the cohomology r ..."
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Cited by 26 (4 self)
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The goal of this article is to motivate and describe how GromovWitten theory can and has provided tools to understand the moduli space of curves. For example, ideas and methods from GromovWitten theory have led to both conjectures and theorems showing that the tautological part of the cohomology ring has a remarkable and profound structure. As an illustration, we describe a new approach to Faber’s intersection number conjecture via branched covers of the projective line (work with I.P. Goulden and D.M. Jackson, based on work with T. Graber). En route we review the work of a large number of mathematicians.
A simple proof of Witten conjecture through localization
"... Abstract. We obtain a system of relations between Hodge integrals with one λclass. As an application, we show that its first nontrivial relation implies the Witten’s Conjecture/Kontsevich Theorem [12, 6]. 1. ..."
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Cited by 25 (8 self)
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Abstract. We obtain a system of relations between Hodge integrals with one λclass. As an application, we show that its first nontrivial relation implies the Witten’s Conjecture/Kontsevich Theorem [12, 6]. 1.
BIRATIONAL COBORDISM INVARIANCE OF UNIRULED SYMPLECTIC MANIFOLDS
, 2006
"... 2. Birational cobordism 3 2.1. Coupling form and linear deformations 4 2.2. Blowup and blowdown 6 ..."
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Cited by 24 (1 self)
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2. Birational cobordism 3 2.1. Coupling form and linear deformations 4 2.2. Blowup and blowdown 6
Invariance of tautological equations I: conjectures and applications
"... Abstract. The main goal of this paper is to introduce a set of conjectures on the relations in the tautological rings. In particular, the conjectures gives an efficient algorithm to calculate, conjecturally, all tautological equations using only finite dimensional linear algebra. Other applications ..."
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Cited by 23 (8 self)
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Abstract. The main goal of this paper is to introduce a set of conjectures on the relations in the tautological rings. In particular, the conjectures gives an efficient algorithm to calculate, conjecturally, 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. 1.
POLYNOMIAL RECURSION FORMULA FOR LINEAR HODGE INTEGRALS
"... Abstract. We establish a polynomial recursion formula for linear Hodge integrals. It is obtained as the cutandjoin equation for the Laplace transform of the Hurwitz numbers. We show that the recursion recovers the WittenKontsevich theorem when restricted to the top degree terms, and also the comb ..."
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Cited by 19 (9 self)
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Abstract. We establish a polynomial recursion formula for linear Hodge integrals. It is obtained as the cutandjoin equation for the Laplace transform of the Hurwitz numbers. We show that the recursion recovers the WittenKontsevich theorem when restricted to the top degree terms, and also the combinatorial factor of the λg formula as the lowest degree terms. Dedicated to Herbert Kurke on the occasion of his 70th birthday Contents