Faculty of Science and Engineering Department of Science
Job title
Professor
Degree
Doctor of Science
Profile
I am studying so-called ``integrable systems'' in mathematics and mathematical physics by the method of algebraic analysis. The aim is to elucidate algebraic, geometric and combinatorial structures hidden in integrable systems, and to apply such knowledge to mathematical physis. My research interest also ranges over some other areas related to integrable systems, such as algebraic combinatorics, Painleve equations and twistor theory. Professor Emeritus of Kyoto University.
Professor, Graduate School of Human and Environmental Studies, Kyoto Univeristy
Apr 1984
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Aug 1985
Research Assistant, Faculty of Science, Saitama University
Sep 1985
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Mar 1991
Research Assistant, Research Institute for Mathematical Sciences, Kyoto University
Apr 1991
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Dec 2003
Associate Professor, College of Liberal Arts; Faculty of Integrated Human Studies; Graduate School of Human and Environmental studies, Kyoto University
Jan 2004
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Mar 2014
Professor, Graduate School of Human and Environmental Studies, Kyoto University
Apr 2014
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Today
Professor, Faculty of Science and Engineering, Kinki University
Commun. Math. Phys. (online in 2019) Dec 2018 [Refereed]
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 generalized shift symmetries in a fermionic realization
of the two-dimens...
J. Phys. A: Math. Theor. 51 (2018), 43LT01 (9 pages) Jun 2018 [Refereed]
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 to be expressed as , where is a...
J. Phys. A: Math. Theor. 51 (2018), 203001 (35pp) Jan 2018 [Refereed]
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) hierarchy can be derived from the 2D Toda hierarchy as
reductions. The...
J. Geom. Phys. 137C (2019), 184-203. Aug 2018 [Refereed]
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 partition function deformed by an infinite number of exter...
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 topological vertex. Open string amplitudes on each
leg of the web diagram o...
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 algebraic relation. This algebraic relation
can be used to identify ...
J. Phys.: Conf. Ser. 482 (2014) 012041 Dec 2013 [Invited]
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 function of the ordinary melting crystal model is
known to become essen...
RIMS Kokyuroku 1913 (2014), pp.182-201 Jan 2013 [Invited]
The notion of topological vertex and the construction of topological string
partition functions on local toric Calabi-Yau 3-folds are reviewed.
Implications of an explicit formula of partition functions for the generalized
conifolds are considered...
poster presentation at conference "Integrability in Gauge and String Theory" (Zurich, August 20-24, 2012) Aug 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...
Mathematical structures of integrable systems, its deepening and expansion 10 Sep 2019 Research Inistitute of Mathematics, Kyoto University
The cubic Hodge integrals are intersection numbers with Hodge classes on the moduli space of complex stable curves. These numbers are labelled by one, two or three integer partitions, and closely related to the topological vertex of topological st...
China-Japan Joint Workshop on Integrable Systems 2019 20 Aug 2019 Daisuke Takahashi (Waseda University) et al.
An important example of Orlov and Scherbin's hypergeometric tau functions is the generating function of the double Hurwitz numbers introduced by Okounkov. Specialization of the second set of the 2D Toda time variables to particular values yields g...
2nd IBS-CGP Workshop on integrable systems and applications 7 May 2019 Alexander Aleksandrov
Around 2003, C.-C. Mellissa Liu, Kefeng Liu and Jian Zhou presented a combinatorial description of two-partition cubic Hodge integrals that generalizes the Marino-Vafa formula for one-partition cubic Hodge integrals. Moreover, Zhou pointed out tha...
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