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Integrable hierarchies and the mirror model of local CP 1. Physica D: Nonlinear Phenomena
, 2011
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Gromov–Witten invariants for mirror orbifolds of simple elliptic singularities, Annales de l’institut Fourier 61
, 2011
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Wconstraints for the total descendant potential of a simple singularity
 Compositio Math
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Contact homology of S1bundles over some symplectically reduced orbifolds
, 2009
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Lagrangian Floer potential of orbifold spheres, preprint
, 2014
"... Abstract. For each sphere with three orbifold points, we construct an algorithm to compute the open GromovWitten potential, which serves as the quantumcorrected LandauGinzburg mirror and is an infinite series in general. This gives the first class of generaltype geometries whose full potentials ..."
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Abstract. For each sphere with three orbifold points, we construct an algorithm to compute the open GromovWitten potential, which serves as the quantumcorrected LandauGinzburg mirror and is an infinite series in general. This gives the first class of generaltype geometries whose full potentials can be computed. As a consequence we obtain an enumerative meaning of mirror maps for elliptic curve quotients. Furthermore, we prove that the open GromovWitten potential is convergent, even in the generaltype cases, and has an isolated singularity at the origin, which is an important ingredient of proving homological mirror symmetry. Contents
On the genus Two Free Energies for Semisimple Frobenius
 Manifold, Russian Journal of Mathematical Physics
"... We represent the genus two free energy of an arbitrary semisimple Frobenius manifold as a sum of contributions associated with dual graphs of certain stable algebraic curves of genus two plus the socalled ”genus two Gfunction”. Conjecturally the genus two Gfunction vanishes for a series of import ..."
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We represent the genus two free energy of an arbitrary semisimple Frobenius manifold as a sum of contributions associated with dual graphs of certain stable algebraic curves of genus two plus the socalled ”genus two Gfunction”. Conjecturally the genus two Gfunction vanishes for a series of important examples of Frobenius manifolds associated with simple singularities as well as for P1orbifolds with positive Euler characteristics. We explain the reasons for such Conjecture and prove it in
GromovWitten theory of Fano orbifold curves, Gamma integral structures and ADEToda Hierarchies
"... Abstract. We construct an integrable hierarchy in the form of Hirota quadratic equations (HQE) that governs the Gromov–Witten (GW) invariants of the Fano orbifold projective curve P1a1,a2,a3 with positive orbifold Euler characteristic. We also identify our HQEs with an appropriate Kac–Wakimoto hiera ..."
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Abstract. We construct an integrable hierarchy in the form of Hirota quadratic equations (HQE) that governs the Gromov–Witten (GW) invariants of the Fano orbifold projective curve P1a1,a2,a3 with positive orbifold Euler characteristic. We also identify our HQEs with an appropriate Kac–Wakimoto hierarchy of ADE type. In particular, we obtain a generalization of the famous Toda conjecture about the GW invariants of P1. Contents