Updated on 2024/10/23
理学博士 （ 1990.3 東京大学 ）
Others / Others / Algebra
cluster algebras
The University of Tokyo Graduate School, Division of Science
- 1990.3
Country： Japan
The University of Tokyo Faculty of Science
- 1985
Country： Japan
日本数学会
DILOGARITHM IDENTITIES IN CLUSTER SCATTERING DIAGRAMS
Nakanishi, T
NAGOYA MATHEMATICAL JOURNAL 2023.12
Asymptotic Sign Coherence Conjecture Reviewed
Gekhtman Michael, Nakanishi Tomoki
EXPERIMENTAL MATHEMATICS Vol. 31 ( 2 ) page： 497 - 505 2022.7
Synchronicity phenomenon in cluster patterns Reviewed
Nakanishi Tomoki
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES Vol. 103 ( 3 ) page： 1120 - 1152 2021.4
Rogers dilogarithms of higher degree and generalized cluster algebras Reviewed
Nakanishi Tomoki
JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN Vol. 70 ( 4 ) page： 1269 - 1304 2018.10
Hamiltonian and Lagrangian formalisms of mutations in cluster algebras and application to dilogarithm identities Reviewed
Michael Gekhtman, Tomoki Nakanishi, Dylan Rupel
J. Integrable Syst. Vol. 2 page： 1-35 2017
Exact WKB analysis and cluster algebras II: simple poles Reviewed
Kohei Iwaki, Tomoki Nakanishi
Int. Math. Res. Not. Vol. 2016 page： 4375--4417 2016
Wonder of sine-Gordon Y-systems Reviewed
Tomoki Nakanishi, Salvatore Stella
Trans. Amer. Math. Soc Vol. 368 page： 6835-6886 2016
Companion cluster algebras to a generalized cluster algebra Invited Reviewed
Tomoki Nakanishi, Dylan Rupel
Travaux mathematiques Vol. 24 page： 129-149 2016
Structure of seeds in generalized cluster algebras Reviewed
Tomoki Nakanishi
Pacific J. Math. Vol. 277 page： 201-218 2015
Quantum generalized cluster algebras and quantum dilogarithms of higher degrees Reviewed
Tomoki Nakanishi
Theor. Math. Phys. Vol. 185 page： 1759--1768 2015
Exact WKB analysis and cluster algebras Reviewed
Kohei Iwaki, Tomoki Nakanishi
J. Phys. A: Math. Theor. Vol. 47 page： 474009 2014
Diagrammatic description of c-vectors and d-vectors of cluster algebras of finite type Reviewed
Tomoki Nakanishi, Salvatore Stella
Electron. J. Combin. Vol. 21 page： #P1.3,107 pages 2014
Periodicities of T and Y-systems, dilogarithm identities, and cluster algebras I: Type B_r Reviewed
Rei Inoue, Osamu Iyama, Bernhard Keller, Atsuo Kuniba, Tomoki Nakanishi
Publ. RIMS Vol. 49 page： 1-42 2013
Periodicities of T and Y-systems, dilogarithm identities, and cluster algebras II: Types C_r, F_4, and G_2 Reviewed
Rei Inoue, Osamu Iyama, Bernhard Keller, Atsuo Kuniba, Tomoki Nakanishi
Publ. RIMS Vol. 49 page： 43-85 2013
On tropical dualities in cluster algebras Reviewed
Tomoki Nakanishi, Andrei Zelevinsky
Contemp. Math. Vol. 565 page： 217-226 2012
Note on dilogarithm identities from nilpotent double affine Hecke algebras Reviewed
Tomoki Nakanishi
SIGMA Vol. 8 page： 104, 5 pages 2012
Tropicalization method in cluster algebras Invited Reviewed
Tomoki Nakanishi
Contemp. Math Vol. 580 page： 95-115 2012
Dilogarithm identities for conformal field theories and cluster algebras: simply laced case Reviewed
Tomoki Nakanishi
Nagoya Math. J. Vol. 202 page： 23-43 2011
T-systems and Y-systems in integrable systems Reviewed
Atsuo Kuniba, Tomoki Nakanishi, Junji Suzuki
J. Phys. A: Math. Theor. Vol. 44 page： 103001 (146pp) 2011
T-systems, Y-systems, and cluster algebras: Tamely laced case Reviewed
Tomoki Nakanishi
Proc. of the Infinite Analysis 09, New Trends in Quantum Integrable Systems, eds. B. Feigin, et al., World Scientific, Singapore page： 325--355 2011
Difference equations and cluster algebras I: Poisson bracket for integrable difference equations Reviewed
Rei Inoue, Tomoki Nakanishi
RIMS Kokyuroku Bessatsu Vol. B28 page： 63-88 2011
On Frenkel-Mukhin algorithm for q-character of quantum affine algebras Reviewed
Wakako Nakai, Tomoki nakanishi
Adv. Pure Math. Vol. 61 page： 327-347 2011
Classical and quantum dilogarithm identities Reviewed
Rinat Kashaev, Tomoki Nakanishi
SIGMA Vol. 7 page： 102, 29 pages 2011
Periodicities in cluster algebras and dilogarithm identities Reviewed
Tomoki Nakanishi
Representations of algebras and related topics (A. Skowronski and K. Yamagata, eds.), EMS Series of Congress Reports, European Mathematical Society page： 407-444 2011
Periodicities of T-systems and Y-systems Reviewed
Rei Inoue, Osamu Iyama, Atsuo Kuniba, Tomoki Nakanishi, Junji Suzuki
Nagoya Math. J. Vol. 197 page： 59-174 2010
Dilogarithm identities for sine-Gordon and reduced sine-Gordon Y-systems Reviewed
Tomoki Nakanishi, Roberto Tateo
SIGMA Vol. 6 page： 085, 34 pages 2010
T-systems and Y-systems for quantum affiniations of quantum Kac-Moody algebras Reviewed
Atsuo Kuniba, Tomoki Nakanishi, Junji Suzuki
SIGMA Vol. 5 page： 108, 23 pages 2009
Paths and tableaux descriptions of Jacobi-Trudi determinant associated with quantum affine algebra of type D_n Reviewed
Wakako Nakai, Tomoki Nakanishi
J. Alg. Combin. Vol. 26 2007
*Paths and tableaux descriptions of Jacobi-Trudi determinant associated with quauntum affine algebra of type C_n Reviewed
Wakako Nakai, Tomoki Nakanishi
SIGMA Vol. 3 2007
Paths, tableuax, and q-characters of quantum affine algebras: the C_n case Reviewed
Wakako Nakai, Tomoki Nakanishi
J. Phys. A: Math, Gen. Vol. 39 2006
*The canonical solutions of the Q-systems and the Kirillov-Reshetikhin conjecture Reviewed
Atsuo Kuniba, Tomoki Nakanishi, Zengo Tsuboi
Commun. Math. Phys. Vol. 227 2002
The Bethe equation at q=0, the Mobius inversion formula, and weight multiplicities III: The X^{(r)}_n case Reviewed
Atsuo Kuniba, Tomoki Nakanishi, Zengo Tsuboi
Lett. Math. Phys. Vol. 59 2002
*The Bethe equation at q=0, the Mobius inversion formula, and weight multiplicities II: The X_n case Reviewed
Atsuo Kuniba, Tomoki Nakanishi
J. Algebra Vol. 251 2002
The Bethe equation at q=0, the Mobius inversion formula, and weight multiplicities I: The sl(2) case Reviewed
Atsuo Kuniba, Tomoki Nakanishi
Progr. in Math. Vol. 191 2000
Skew Young diagram method in spectral decomposition of integrable lattice models II: Higher levels Reviewed
Anatol N. Kirillov, Atsuo Kuniba, Tomoki Nakanishi
Nucl. Phys. B Vol. 529 page： 611-638 1998
Skew Young diagram method in spectral decomposition of integrable lattice models Reviewed
Anatol N. Kirillov, Atsuo Kuniba, Tomoki Nakanishi
Commun. Math. Phys Vol. 185 page： 441-465 1997
Spectral decomposition of path space in solvable lattice models Reviewed
Tomoyuki Arakawa, Tomoki Nakanishi, Kazuyuki Oshima, Akihiro Tsuchiya
Commun. Math. Phys Vol. 181 1996
Fusion, mass, and representation theory of Yangian Reviewed
Tomoki Nakanishi
Nuclear Physics B Vol. 439 page： 441-459 1995
*Functional relations in solvable lattice models I:Functional relations and representation theory Reviewed
Atsuo Kuniba, Tomoki Nakanishi, Junji Suzuki
Int. J. Mod. Phys. A Vol. 9 page： 5215-5266 1994
Functional relations in solvable lattice models II: Applications Reviewed
Atsuo Kuniba, Tomoki Nakanishi, Junji Suzuki
Int. J. Mod. Phys. A Vol. 9 page： 5267-5312 1994
Characters in conformal field theories from thermodynamic Bethe ansatz Reviewed
Atsuo Kuniba, Tomoki Nakanishi, Junji Suzuki
Mod. Phys. Lett. A Vol. 8 page： 1649-1659 1993
Rogers dilogarithm in integrable systems Reviewed
Atsuo Kuniba, Tomoki Nakanishi
Differential Geometric Methods in Theoretical Physics: Proceedings of the XXI International Conference (M.-L. Ge et al., eds.), World Scientific, Singapore page： 419--422 1993
Fusion RSOS models and rationalc coset models Reviewed
Atsuo Kuniba, Tomoki Nakanishi
Lecture Note in Math. page： 1510 1992
Spectra in conformal field theories from the Rogers dilogarithm Reviewed
Atsuo Kuniba, Tomoki Nakanishi
Mod. Phys. Lett. A Vol. 7 page： 3487-3494 1992
The annihilating ideals of minimal models Reviewed
Boris L. Feigin, Tomoki Nakanishi, Hirosi Ooguri
International Journal of Modern Physics A Vol. 7 page： 1A 1992
*Level-rank duality in WZW models in confomal field theory Reviewed
Tomoki Nakanishi, Akihiro Tsuchiya
Communication in Maihematical Physics page： 144 1992
Fusion algebras in integrable systems in tew dimension Reviewed
Frederick M. Goodman, Tomoki Nakanishi
Physics letters B page： 262 1991
Yang-Baxter eguation for the sl(n) chiral Potts model Reviewed
Rinat Kashaev, Vladimir V. Mangazeev, Tomoki Nakanishi
Nuclear Physics B page： 362 1991
Ferro-and antiferro-magnetization in RSOS models Reviewed
Atsuo Kuniba, Tomoki Nakanishi, Junji Suzuki
Nuclear Physics B page： 356 1991
Level-rank duality in fusion RSOS models Reviewed
Atsuo Kuniba, Tomoki Nakanishi
International Colloquium on Modern Quantum Field Theory (S. Das et al., eds.), World Scientific, Singapore page： 344-374 1991
Non-unitary minimal models and RSOSS MODELS Reviewed
Tomoki Nakanishi
Nuclear Physics B page： 334 1990
Radical root structure of conformal algebra Reviewed
Tomoki Nakanishi
Proyress of Theoutical Physice page： 82 1989
Differential equations in g>=2 conformal field theory Reviewed
Akishi Kato, Tomoki Nakanishi
Modern Physics letters A page： 4 1989
Generalized Supersummrtry in Riemann surfaces and the associated string models Reviewed
Tomoki Nakanishi
Modern Physics letters A page： 3 1988
Cluster algebras and scattering diagrams Reviewed
Tomoki Nakanishi（ Role： Sole author）
Mathematical Society of Japan 2023.3 （ ISBN:978-4-86497-105-8 ）
団代数・ルート系・散乱図式 Invited
中西知樹
日本数学会２０２１年度年会（企画特別講演） 2021.3
Grant number：23KF0144 2023.9 - 2025.3
科学研究費助成事業 特別研究員奨励費
中西 知樹, CAO PEIGEN
Authorship：Principal investigator
Grant amount：\600000 （ Direct Cost: \600000 ）
Gross-Hacking-Keel-Kontsevitch(GHKK)による団散乱図の導入と(団代数の基盤構造である) 団パターンとの関係に関する画期的な仕事により，団散乱図の構造を通して団パターンの局所 及び大域的な構造を調べることが可能となった.一方，団散乱図には悪地(Badlands)と呼ば れる団パターンのG扇の補集合が存在し，その局所及び大域的な構造は極めて複雑であることがわかっている一方で具体的な様子はほとんど解明されていない．本研究は，これらの問題の解決を目指すものである．
Integration of cluster algebras and scattering diagrams
Grant number：22H01114 2022.4 - 2027.3
Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)
Authorship：Principal investigator
Grant amount：\15340000 （ Direct Cost: \11800000 、 Indirect Cost：\3540000 ）
Integration of cluster algebras and scattering diagrams
Grant number：23K22385 2022.4 - 2027.3
Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)
Authorship：Principal investigator
Grant amount：\15340000 （ Direct Cost: \11800000 、 Indirect Cost：\3540000 ）
Study of new algebraic and combinatorial structure in integrable systems
Grant number：16H03922 2016.4 - 2021.3
Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)
Nakanishi Tomoki
Authorship：Principal investigator
Grant amount：\17940000 （ Direct Cost: \13800000 、 Indirect Cost：\4140000 ）
We study theory and applications of cluster algebras which is one of algebraic and combinatorial structure in integrable systems. We obtain the following new results and insights: derivation of dilogarithm identities in cluster algebras by classical mechanical method, systematic proofs of synchronicity phenomenon and related conjectures, derivation of the relation between cluster algebra theory and scattering diagrams in the cluster algebraic point of view, proof that any consistency relation in a cluster scattering diagram is generated by the pentagon identity among dilogarithm elements, dilogarithm identities associated to cluster scattering diagrams and their quantizations, derivation of product formula of F-polynomials.
量子群の表現と量子可積分系
2007
科学研究費補助金 基盤研究（Ｃ）（一般），課題番号：19540021
中西 知樹
Authorship：Principal investigator
Linear Algebra II
2011
Linear Algebra I
2011
