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A mathematical theory of the topological vertex
We have developed a mathematical theory of the topological vertex--a theory that was original proposed by M. Aganagic, A. Klemm, M. Marino, and C. Vafa in hep-th/0305132 on effectively computing…
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Topological string partition functions as equivariant indices
We propose to use the identification of topological string partition functions as equivariant indices on framed moduli spaces of instantons to study the Gopakumar-Vafa conjecture for some local…
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Explicit Formula for Witten-Kontsevich Tau-Function
We present an explicit formula for Witten-Kontsevich tau-function.
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A formula of two-partition Hodge integrals
JMg,n where tpi = ci(L?) is the first Chern class of L?, and Xj = Cj(E) is the j-th Chern class of the Hodge bundle. The study of Hodge integrals is an important part of intersection theory on Mg,n>…
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Emergent Geometry and Mirror Symmetry of A Point
By considering the partition function of the topological 2D gravity, a conformal field theory on the Airy curve emerges as the mirror theory of Gromov-Witten theory of a point. In particular, a…
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Local Mirror Symmetry for One-Legged Topological Vertex
We prove the Bouchard-Mari\~no Conjecture for the framed one-legged topological vertex by deriving the Eynard-Orantin type recursion relations from the cut-and-join equation satisfied by the relevant…
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A Conjecture on Hodge Integrals
We propose a conjectural formula expressing the generating series of some Hodge integrals in terms of representation theory of Kac-Moody algebras. Such generating series appear in calculations of…
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Orbifold Hodge numbers of the wreath product orbifolds
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Curve counting and instanton counting
We prove some combinatorial results required for the proof of the following conjecture of Nekrasov: The generating function of closed string invariants in local Calabi-Yau geometries obtained by…
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A Proof of a Conjecture of Marino-Vafa on Hodge Integrals
We prove a remarkable formula for Hodge integrals conjectured by Marino and Vafa based on large N duality, using functorial virtual localization on certain moduli spaces of relative stable morphisms.
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