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42
Computation of open GromovWitten invariants for toric CalabiYau 3folds by topological recursion, a proof of the BKMP conjecture
, 2013
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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
Open topological strings and integrable hierarchies: Remodeling the amodel
, 2011
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Invariants of spectral curves and intersection theory of moduli spaces of complex curves
, 2011
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The spectral curve and the Schrödinger equation of double Hurwitz numbers and higher spin structures
"... Abstract. We derive the spectral curves for qpart double Hurwitz numbers, rspin simple Hurwitz numbers, and arbitrary combinations of these cases, from the analysis of the unstable (0, 1)geometry. We quantize this family of spectral curves and obtain the Schrödinger equations for the partition fun ..."
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Cited by 10 (8 self)
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Abstract. We derive the spectral curves for qpart double Hurwitz numbers, rspin simple Hurwitz numbers, and arbitrary combinations of these cases, from the analysis of the unstable (0, 1)geometry. We quantize this family of spectral curves and obtain the Schrödinger equations for the partition function of the corresponding Hurwitz problems. We thus confirm the conjecture for the existence of quantum curves in these generalized Hurwitz number cases.
Topological recursion for the Poincare polynomial of the combinatorial moduli space of curves
, 2010
"... We show that the Poincare polynomial associated with the orbifold cell decomposition of the moduli space of smooth algebraic curves with distinct marked points satisfies a topological recursion formula of the EynardOrantin type. The recursion uniquely determines the Poincaré polynomials from the ..."
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Cited by 10 (4 self)
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We show that the Poincare polynomial associated with the orbifold cell decomposition of the moduli space of smooth algebraic curves with distinct marked points satisfies a topological recursion formula of the EynardOrantin type. The recursion uniquely determines the Poincaré polynomials from the initial data. Our key discovery is that the Poincare ́ polynomial is the Laplace transform of the number of Grothendieck’s dessins d’enfants.
THE SPECTRAL CURVE OF THE EYNARDORANTIN RECURSION VIA THE LAPLACE TRANSFORM
"... Abstract. The EynardOrantin recursion formula provides an effective tool for certain enumeration problems in geometry. The formula requires a spectral curve and the recursion kernel. We present a uniform construction of the spectral curve and the recursion kernel from the unstable geometries of th ..."
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Cited by 9 (2 self)
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Abstract. The EynardOrantin recursion formula provides an effective tool for certain enumeration problems in geometry. The formula requires a spectral curve and the recursion kernel. We present a uniform construction of the spectral curve and the recursion kernel from the unstable geometries of the original counting problem. We examine this construction using four concrete examples: Grothendieck’s dessins d’enfants (or highergenus analogue of the Catalan numbers), the intersection numbers of tautological cotangent classes on the moduli stack of stable pointed curves, single Hurwitz numbers, and the stationary GromovWitten invariants of the complex projective line. Contents