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14
Open topological strings and integrable hierarchies: Remodeling the amodel
, 2011
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Rational reductions of the 2DToda hierarchy and mirror symmetry. Preprint available at 1401.5725
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Cited by 5 (2 self)
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Rational reductions of the 2DToda hierarchy and mirror symmetry
Frobenius structures on double Hurwitz spaces. Preprint available at 1210.2312
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Integrable structure of modified melting crystal model
, 2012
"... Our previous work on a hidden integrable structure of the melting crystal model (the U(1) Nekrasov function) is extended to a modified crystal model. As in the previous case, “shift symmetries ” of a quantum torus algebra plays a central role. With the aid of these algebraic relations, the partition ..."
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Our previous work on a hidden integrable structure of the melting crystal model (the U(1) Nekrasov function) is extended to a modified crystal model. As in the previous case, “shift symmetries ” of a quantum torus algebra plays a central role. With the aid of these algebraic relations, the partition function of the modified model is shown to be a tau function of the 2D Toda hierarchy. We conjecture that this tau function belongs to a class of solutions (the so called Toeplitz reduction) related to the AblowitzLadik hierarchy. 1
Classical rmatrix like approach to Frobenius manifolds, WDVV equations and flat metrics. Preprint arXiv: mathph/1304.2075
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Old and New Reductions of Dispersionless Toda Hierarchy
 SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS
, 2012
"... This paper is focused on geometric aspects of two particular types of finitevariable reductions in the dispersionless Toda hierarchy. The reductions are formulated in terms of “Landau–Ginzburg potentials ” that play the role of reduced Lax functions. One of them is a generalization of Dubrovin and ..."
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This paper is focused on geometric aspects of two particular types of finitevariable reductions in the dispersionless Toda hierarchy. The reductions are formulated in terms of “Landau–Ginzburg potentials ” that play the role of reduced Lax functions. One of them is a generalization of Dubrovin and Zhang’s trigonometric polynomial. The other is a transcendental function, the logarithm of which resembles the waterbag models of the dispersionless KP hierarchy. They both satisfy a radial version of the Löwner equations. Consistency of these Löwner equations yields a radial version of the Gibbons–Tsarev equations. These equations are used to formulate hodograph solutions of the reduced hierarchy. Geometric aspects of the Gibbons–Tsarev equations are explained in the language of classical differential geometry (Darboux equations, Egorov metrics and Combescure transformations). Flat coordinates of the underlying Egorov metrics are presented.