467 citations · 2k across the 86 of their papers we have counts for
27 papers · 1 filter
Dressing operators in equivariant Gromov-Witten theory of
Kanehisa Takasaki
Okounkov and Pandharipande proved that the equivariant Toda hierarchy governs the equivariant Gromov-Witten theory of . A technical clue of their method is a pair of…
Integrable structures of specialized hypergeometric tau functions
Kanehisa Takasaki
Okounkov's generating function of the double Hurwitz numbers of the Riemann sphere is a hypergeometric tau function of the 2D Toda hierarchy in the sense of Orlov and Scherbin. Thi…
Cubic Hodge integrals and integrable hierarchies of Volterra type
Kanehisa Takasaki
A tau function of the 2D Toda hierarchy can be obtained from a generating function of the two-partition cubic Hodge integrals. The associated Lax operators turn out to satisfy an a…
Three-partition Hodge integrals and the topological vertex
Toshio Nakatsu, Kanehisa Takasaki
A conjecture on the relation between the cubic Hodge integrals and the topological vertex in topological string theory is resolved. A central role is played by the notion of genera…
Hurwitz numbers and integrable hierarchy of Volterra type
Kanehisa Takasaki
A generating function of the single Hurwitz numbers of the Riemann sphere is a tau function of the lattice KP hierarchy. The associated Lax operator turns out t…
Toda hierarchies and their applications
Kanehisa Takasaki
The 2D Toda hierarchy occupies a central position in the family of integrable hierarchies of the Toda type. The 1D Toda hierarchy and the Ablowitz-Ladik (aka relativistic Toda) hie…
4D limit of melting crystal model and its integrable structure
Kanehisa Takasaki
This paper addresses the problems of quantum spectral curves and 4D limit for the melting crystal model of 5D SUSY Yang-Mills theory on . The partiti…
-Difference Kac-Schwarz Operators in Topological String Theory
Kanehisa Takasaki, Toshio Nakatsu
The perspective of Kac-Schwarz operators is introduced to the authors' previous work on the quantum mirror curves of topological string theory in strip geometry and closed topologi…
Open string amplitudes of closed topological vertex
Kanehisa Takasaki, Toshio Nakatsu
The closed topological vertex is the simplest ``off-strip'' case of non-compact toric Calabi-Yau threefolds with acyclic web diagrams. By the diagrammatic method of topological ver…
Orbifold melting crystal models and reductions of Toda hierarchy
Kanehisa Takasaki
Orbifold generalizations of the ordinary and modified melting crystal models are introduced. They are labelled by a pair of positive integers, and geometrically related to $\…
Modified melting crystal model and Ablowitz-Ladik hierarchy
Kanehisa Takasaki
This is a review of recent results on the integrable structure of the ordinary and modified melting crystal models. When deformed by special external potentials, the partition func…
Generalized Ablowitz-Ladik hierarchy in topological string theory
Kanehisa Takasaki
This paper addresses the issue of integrable structures in topological string theory on generalized conifolds. Open string amplitudes of this theory can be expressed as the matrix…
Modified melting crystal model and Ablowitz-Ladik hierarchy
Kanehisa Takasaki
This paper addresses the issue of integrable structure in a modified melting crystal model of topological string theory on the resolved conifold. The partition function can be expr…
Remarks on partition functions of topological string theory on generalized conifolds
Kanehisa Takasaki
The method of topological vertex for topological string theory on toric Calabi-Yau 3-folds is reviewed. Implications of an explicit formula of partition functions in the "on-strip"…
Integrable structure of modified melting crystal model
Kanehisa Takasaki
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, "shif…
Old and New Reductions of Dispersionless Toda Hierarchy
Kanehisa Takasaki
This paper is focused on geometric aspects of two particular types of finite-variable reductions in the dispersionless Toda hierarchy. The reductions are formulated in terms of "La…
Pfaffian structures and certain solutions to BKP hierarchies I. Sums over partitions
A. Yu. Orlov, T. Shiota, K. Takasaki
We introduce a useful and rather simple class of BKP tau functions which which we shall call "easy tau functions". We consider two versions of BKP hierarchy, one we will call "smal…
An hbar-expansion of the Toda hierarchy: a recursive construction of solutions
Kanehisa Takasaki, Takashi Takebe
A construction of general solutions of the \hbar-dependent Toda hierarchy is presented. The construction is based on a Riemann-Hilbert problem for the pairs (L,M) and (\bar L,\bar…
Thermodynamic limit of random partitions and dispersionless Toda hierarchy
Kanehisa Takasaki, Toshio Nakatsu
We study the thermodynamic limit of random partition models for the instanton sum of 4D and 5D supersymmetric U(1) gauge theories deformed by some physical observables. The physica…
hbar-Dependent KP hierarchy
Kanehisa Takasaki, Takashi Takebe
This is a summary of a recursive construction of solutions of the hbar-dependent KP hierarchy. We give recursion relations for the coefficients X_n of an hbar-expansion of the oper…
Toda tau functions with quantum torus symmetries
Kanehisa Takasaki
The quantum torus algebra plays an important role in a special class of solutions of the Toda hierarchy. Typical examples are the solutions related to the melting crystal model of…
Generalized string equations for double Hurwitz numbers
Kanehisa Takasaki
The generating function of double Hurwitz numbers is known to become a tau function of the Toda hierarchy. The associated Lax and Orlov-Schulman operators turn out to satisfy a set…
Non-degenerate solutions of universal Whitham hierarchy
Kanehisa Takasaki, Takashi Takebe, Lee Peng Teo
The notion of non-degenerate solutions for the dispersionless Toda hierarchy is generalized to the universal Whitham hierarchy of genus zero with marked points. These solutio…
KP and Toda tau functions in Bethe ansatz
Kanehisa Takasaki
Recent work of Foda and his group on a connection between classical integrable hierarchies (the KP and 2D Toda hierarchies) and some quantum integrable systems (the 6-vertex model…