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# Kanehisa TAKASAKI

Last updated: May 14, 2019 at 22:50

Name Kanehisa TAKASAKI takasakimath.kindai.ac.jp http://www2.yukawa.kyoto-u.ac.jp/~kanehisa.takasaki/index-e.html Kindai University Faculty of Science and Engineering　Department of Science Professor 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 enumerative combinatorics, Painleve equations and twistor theory. Professor Emeritus of Kyoto University.

## 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
-
Today
Professor, Faculty of Science and Engineering, Kinki University

## Education

Apr 1975
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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

1998
Daiwa Adrian Prize (jointly awarded), Daiwa Anglo-Japan Foundation
Winner: Ryu Sasaki et al.

## Published Papers

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
is a tau function of the lattice KP hierarchy. The associated
Lax operator turns out to be expressed as , where
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 Yang-Mills theory on . The partition function 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, Toshio Nakatsu
J. Phys. A: Math. Theor. 49 (2016), 025201 (28 pages)      Dec 2015   [Refereed]
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 vertex, open string amplitudes of topological string theory therein ca...

## Misc

Toshio Nakatsu, Kanehisa Takasaki
Dec 2018
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...
Integrable systems and Calabi-Yau varieties
Kanehisa TAKASAKI
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

 線形代数とネットワーク高崎金久Mar 2017   ISBN:4535788294
 学んでみよう! 記号論理高崎金久日本評論社   Aug 2014   ISBN:4535787603
 復刊 可積分系の世界 ―戸田格子とその仲間―高崎 金久共立出版   Jul 2013   ISBN:4320110420
 線形代数と数え上げ高崎 金久日本評論社   Jun 2012   ISBN:4535786801
 現代数理科学事典 第2版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

Kanehisa TAKASAKI
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...
Kanehisa TAKASAKI
72nd Encounter with Mathematics   12 Jan 2019   Department of Mathematics, Chuo University
Kanehisa TAKASAKI
SIDE13   13 Nov 2018   SIDE13 organizing committee
Some results on Toda-type equations and Nekrasov partitions functions are presented.
Kanehisa TAKASAKI
AIMS Conferencer 2018   7 Jul 2018   American Institute of Mathematical Sciences
This talk presents recent results on integrable structures in generating functions of Hurwitz numbers. Ref: arXiv:1807.00085T.
Kanehisa TAKASAKI
Seminar of IBS Center of Geometry and Physics   27 Mar 2018   IBS Center of Geometry and Physics
The melting crystal model is a model of statistical mechanics
for random 3D Young diagrams. The partition function of this model
may be thought of as a -deformation of the generating function
of stationary Gromov-Witten invariants of \$\mathbf{...

## 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