Related papers: Topological recursion and mirror curves

We present here the K-theoretic version of mirror models of toric manifold. First, we recall the construction of cohomological mirrors for toric manifolds, i.e. representations of the toric hypergeometric functions from quantum cohomology…

Gromov-Witten theory is used to define an enumerative geometry of curves in Calabi-Yau 5-folds. We find recursions for meeting numbers of genus 0 curves, and we determine the contributions of moving multiple covers of genus 0 curves to the…

We define an integer-valued virtual count of embedded pseudo-holomorphic curves of two times a primitive homology class and arbitrary genus in symplectic Calabi--Yau $3$-folds, which can be viewed as an extension of Taubes' Gromov…

We propose a complete, new formalism to compute unambiguously B-model open and closed amplitudes in local Calabi-Yau geometries, including the mirrors of toric manifolds. The formalism is based on the recursive solution of matrix models…

We prove that every degree-g polynomial in the $\psi$-classes on $\overline{\mathcal M}_{g, n}$ can be expressed as a sum of tautological classes supported on the boundary with no $\kappa$-classes. Such equations, which we refer to as…

We compute certain open Gromov-Witten invariants for toric Calabi-Yau threefolds. The proof relies on a relation for ordinary Gromov-Witten invariants for threefolds under certain birational transformation, and a recent result of Kwokwai…

We study the web of dualities relating various enumerative invariants, notably Gromov-Witten invariants and invariants that arise in topological gauge theory. In particular, we study Donaldson-Thomas gauge theory and its reductions to D=4…

The paper contains some new results and a review of recent achievements, concerning the multisupport solutions to matrix models. In the leading order of the 't Hooft expansion for matrix integral, these solutions are described by…

We find an explicit matrix model computing the refined topological vertex, starting from its representation in terms of plane partitions. We then find the spectral curve of that matrix model, and thus the mirror symmetry of the refined…

We prove that the Borcea-Voisin mirror pairs of Calabi-Yau threefolds admit projective birational models that satisfy the Berglund-H\"ubsch-Chiodo-Ruan transposition rule. This shows that the two mirror constructions provide the same mirror…

This article accompanies my June 1998 seminaire Bourbaki talk on Givental's work. After a quick review of descendent integrals in Gromov-Witten theory, I discuss Givental's formalism relating hypergeometric series to solutions of quantum…

We introduce and analyze free energy landscapes defined by associating to any point inside the sphere a free energy calculated on a thin spherical band around it, using many orthogonal replicas. This allows us to reinterpret, rigorously…

This is the first of two papers which construct a purely algebraic counterpart to the theory of Gromov-Witten invariants (at all genera). These Gromov-Witten type invariants depend on a Calabi-Yau A-infinity category, which plays the role…

We provide an integral formula for the free energy of the two-matrix model with polynomial potentials of arbitrary degree (or formal power series). This is known to coincide with the tau-function of the dispersionless two--dimensional Toda…

The moduli space of stable quotients introduced by Marian-Oprea-Pandharipande provides a natural compactification of the space of morphisms from nonsingular curves to a nonsingular projective variety and carries a natural virtual class. We…

In this paper we demonstrate that the Stokes constants of unrefined free energies and the Stokes constants of Nekrasov-Shatashvili free energies of topological string on a non-compact Calabi-Yau threefold are identical, possibly up to a…

We prove the equivariant Gromov-Witten theory of a nonsingular toric 3-fold X with primary insertions is equivalent to the equivariant Donaldson-Thomas theory of X. As a corollary, the topological vertex calculations by Agangic, Klemm,…

We prove that for a compact toric manifold whose anti-canonical divisor is numerically effective, the Lagrangian Floer superpotential defined by Fukaya-Oh-Ohto-Ono is equal to the superpotential written down by using the toric mirror map…

We prove the existence of a continuous Morse energy function for an arbitrary topological flow with finite hyperbolic (in topological sense) chain recurrent set on a topological manifold of any dimension. This result is a partial solution…

Symplectic invariants introduced in math-ph/0702045 can be computed for an arbitrary spectral curve. For some examples of spectral curves, those invariants can solve loop equations of matrix integrals, and many problems of enumerative…