J-GLOBAL         Last updated: Dec 7, 2019 at 12:44
Kindai University
Faculty of Science and Engineering Department of Science
Job title
Doctor of Science


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.

Research Areas


Academic & Professional Experience

Jan 2004
Mar 2014
Professor, Graduate School of Human and Environmental Studies, Kyoto Univeristy
Apr 1984
Aug 1985
Research Assistant, Faculty of Science, Saitama University
Sep 1985
Mar 1991
Research Assistant, Research Institute for Mathematical Sciences, Kyoto University
Apr 1991
Dec 2003
Associate Professor, College of Liberal Arts; Faculty of Integrated Human Studies; Graduate School of Human and Environmental studies, Kyoto University
Jan 2004
Mar 2014
Professor, Graduate School of Human and Environmental Studies, Kyoto University
Apr 2014
Professor, Faculty of Science and Engineering, Kinki University


Apr 1975
Mar 1979
Department of Mathematics, Faculty of Science, University of Tokyo
Apr 1979
Mar 1984
Division of Mathematics, Graduate School of Sciences, University of Tokyo

Awards & Honors

Daiwa Adrian Prize (jointly awarded), Daiwa Anglo-Japan Foundation
Winner: Ryu Sasaki et al.

Published Papers

Toshio Nakatsu, Kanehisa Takasaki
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...
Kanehisa Takasaki
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
Tex is a tau function of the lattice KP hierarchy. The associated
Lax operator Tex turns out to be expressed as Tex, where
Tex is a...
Kanehisa Takasaki
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...
Kanehisa Takasaki
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 Tex Yang-Mills theory on Tex. The partition function Tex deformed by an infinite number of exter...
Kanehisa Takasaki, Toshio Nakatsu
SIGMA 13 (2017), 009, 28 pages      Sep 2016   [Refereed]
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...


Kanehisa Takasaki
   Sep 2019
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 ...
Integrable systems and Calabi-Yau varieties
Suri Kagaku No. 666, pp. 61-66      Oct 2018   [Invited]
Kanehisa Takasaki
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...
Kanehisa Takasaki
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...
Kanehisa Takasaki
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...

Books etc

Mar 2017   ISBN:4535788294
日本評論社   Aug 2014   ISBN:4535787603
高崎 金久
共立出版   Jul 2013   ISBN:4320110420
高崎 金久
日本評論社   Jun 2012   ISBN:4535786801
現代数理科学事典編集委員会 (Part:Contributor, ソリトン)
丸善   Dec 2009   ISBN:462108125X

Conference Activities & Talks

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...
72nd Encounter with Mathematics   12 Jan 2019   Department of Mathematics, Chuo University
SIDE13   13 Nov 2018   SIDE13 organizing committee
Some results on Toda-type equations and Nekrasov partitions functions are presented.

Research Grants & Projects

Ministry of Education, Culture, Sports, Science: Grant-in-Aid for Scientific Research
Project Year: 2018 - 2021    Investigator(s): Kanehisa TAKASAKI
Ministry of Education, Culture, Sports, Science: Grant-in-Aid for Scientific Research
Project Year: 2013 - 2017    Investigator(s): Kanehisa Takasaki
Ministry of EduMinistry of Education, Culture, Sports, Science and Technology: Grant-in-Aid for Scientific Research
Project Year: 2010 - 2012    Investigator(s): Kanehisa TAKASAKI
Ministry of Education, Culture, Sports, Science and Technology: Grants-in-Aid for Scientific Research(基盤研究(C))
Project Year: 2007 - 2009    Investigator(s): Kanehisa TAKASAKI
Ministry of Education, Culture, Sports, Science and Technology: Grants-in-Aid for Scientific Research(基盤研究(B))
Project Year: 2004 - 2006    Investigator(s): Kanehisa TAKASAKI