Updated on 2022/03/28

写真a

 
NAKANISHI, Tomoki
 
Organization
Graduate School of Mathematics Division of Mathematics Natural Mathematics Professor
Graduate School
Graduate School of Mathematics
Undergraduate School
School of Science Department of Mathematics
Title
Professor
Contact information
メールアドレス

Degree 1

  1. 理学博士 ( 1990.3   東京大学 ) 

Research Areas 1

  1. Others / Others  / Algebra

Current Research Project and SDGs 1

  1. cluster algebras

Education 2

  1. The University of Tokyo   Graduate School, Division of Science

    - 1990.3

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    Country: Japan

  2. The University of Tokyo   Faculty of Science

    - 1985

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    Country: Japan

Professional Memberships 1

  1. 日本数学会

 

Papers 53

  1. Synchronicity phenomenon in cluster patterns Reviewed

    Nakanishi Tomoki

    JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES   Vol. 103 ( 3 ) page: 1120 - 1152   2021.4

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    Language:Japanese  

    DOI: 10.1112/jlms.12402

    Web of Science

  2. Asymptotic Sign Coherence Conjecture Reviewed

    Gekhtman Michael, Nakanishi Tomoki

    EXPERIMENTAL MATHEMATICS     2019.8

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  3. 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

  4. 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

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1093/integr/xyx005

  5. Exact WKB analysis and cluster algebras II: simple poles Reviewed

    Kohei Iwaki, Tomoki Nakanishi

    Int. Math. Res. Not.   Vol. 2016   page: 4375--4417   2016

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    Language:English   Publishing type:Research paper (scientific journal)  

  6. Wonder of sine-Gordon Y-systems Reviewed

    Tomoki Nakanishi, Salvatore Stella

    Trans. Amer. Math. Soc   Vol. 368   page: 6835-6886   2016

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    Language:English   Publishing type:Research paper (scientific journal)  

  7. Companion cluster algebras to a generalized cluster algebra Invited Reviewed

    Tomoki Nakanishi, Dylan Rupel

    Travaux mathematiques   Vol. 24   page: 129-149   2016

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    Language:English   Publishing type:Research paper (scientific journal)  

  8. Structure of seeds in generalized cluster algebras Reviewed

    Tomoki Nakanishi

    Pacific J. Math.   Vol. 277   page: 201-218   2015

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    Language:English   Publishing type:Research paper (scientific journal)  

  9. Quantum generalized cluster algebras and quantum dilogarithms of higher degrees Reviewed

    Tomoki Nakanishi

    Theor. Math. Phys.   Vol. 185   page: 1759--1768   2015

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    Language:English   Publishing type:Research paper (scientific journal)  

  10. 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

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    Language:English   Publishing type:Research paper (scientific journal)  

  11. Exact WKB analysis and cluster algebras Reviewed

    Kohei Iwaki, Tomoki Nakanishi

    J. Phys. A: Math. Theor.   Vol. 47   page: 474009   2014

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    Language:English   Publishing type:Research paper (scientific journal)  

  12. 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

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    Language:English   Publishing type:Research paper (scientific journal)  

  13. 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

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    Language:English   Publishing type:Research paper (scientific journal)  

  14. On tropical dualities in cluster algebras Reviewed

    Tomoki Nakanishi, Andrei Zelevinsky

    Contemp. Math.   Vol. 565   page: 217-226   2012

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    Language:English   Publishing type:Research paper (scientific journal)  

  15. Note on dilogarithm identities from nilpotent double affine Hecke algebras Reviewed

    Tomoki Nakanishi

    SIGMA   Vol. 8   page: 104, 5 pages   2012

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    Language:English   Publishing type:Research paper (scientific journal)  

  16. Tropicalization method in cluster algebras Invited Reviewed

    Tomoki Nakanishi

    Contemp. Math   Vol. 580   page: 95-115   2012

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    Language:English   Publishing type:Research paper (scientific journal)  

  17. Dilogarithm identities for conformal field theories and cluster algebras: simply laced case Reviewed

    Tomoki Nakanishi

    Nagoya Math. J.   Vol. 202   page: 23-43   2011

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    Language:English   Publishing type:Research paper (scientific journal)  

  18. 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

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    Language:English   Publishing type:Research paper (scientific journal)  

  19. 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

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    Language:English   Publishing type:Research paper (scientific journal)  

  20. 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

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    Language:English   Publishing type:Research paper (scientific journal)  

  21. Classical and quantum dilogarithm identities Reviewed

    Rinat Kashaev, Tomoki Nakanishi

    SIGMA   Vol. 7   page: 102, 29 pages   2011

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    Language:English   Publishing type:Research paper (scientific journal)  

  22. 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

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    Language:English   Publishing type:Research paper (scientific journal)  

  23. 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

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    Language:English   Publishing type:Research paper (scientific journal)  

  24. 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

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    Language:English   Publishing type:Research paper (scientific journal)  

  25. Dilogarithm identities for sine-Gordon and reduced sine-Gordon Y-systems Reviewed

    Tomoki Nakanishi, Roberto Tateo

    SIGMA   Vol. 6   page: 085, 34 pages   2010

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    Language:English   Publishing type:Research paper (scientific journal)  

  26. 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

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    Language:English   Publishing type:Research paper (scientific journal)  

  27. 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

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    Language:English   Publishing type:Research paper (scientific journal)  

    We study the Jacobi-Trudi-type determinat which is conjectured to be the q-characters of a certain, in many cases irreducible, finite-dimensional representation of the quantum affine algebra of type D_n. We obtain an expression by a positive sum over a set of tuples of paths, which is naturally translated into the one over a set of tableaux on a skew diagram.

  28. *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

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    Language:English   Publishing type:Research paper (scientific journal)  

  29. 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

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    Language:English   Publishing type:Research paper (scientific journal)  

  30. *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

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    Language:English   Publishing type:Research paper (scientific journal)  

  31. 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

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    Language:English   Publishing type:Research paper (scientific journal)  

  32. *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

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    Language:English   Publishing type:Research paper (scientific journal)  

  33. 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

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    Language:English   Publishing type:Research paper (scientific journal)  

  34. 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

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    Language:English   Publishing type:Research paper (scientific journal)  

  35. 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

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    Language:English   Publishing type:Research paper (scientific journal)  

  36. Spectral decomposition of path space in solvable lattice models Reviewed

    Tomoyuki Arakawa, Tomoki Nakanishi, Kazuyuki Oshima, Akihiro Tsuchiya

    Commun. Math. Phys   Vol. 181   1996

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    Language:English   Publishing type:Research paper (scientific journal)  

  37. Fusion, mass, and representation theory of Yangian Reviewed

    Tomoki Nakanishi

    Nuclear Physics B   Vol. 439   page: 441-459   1995

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    Language:English   Publishing type:Research paper (scientific journal)  

  38. *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

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  39. 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

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  40. 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

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  41. 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

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    Language:English   Publishing type:Research paper (scientific journal)  

  42. Fusion RSOS models and rationalc coset models Reviewed

    Atsuo Kuniba, Tomoki Nakanishi

    Lecture Note in Math.     page: 1510   1992

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  43. Spectra in conformal field theories from the Rogers dilogarithm Reviewed

    Atsuo Kuniba, Tomoki Nakanishi

    Mod. Phys. Lett. A   Vol. 7   page: 3487-3494   1992

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    Language:English   Publishing type:Research paper (scientific journal)  

  44. 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

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  45. *Level-rank duality in WZW models in confomal field theory Reviewed

    Tomoki Nakanishi, Akihiro Tsuchiya

    Communication in Maihematical Physics     page: 144   1992

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  46. Fusion algebras in integrable systems in tew dimension Reviewed

    Frederick M. Goodman, Tomoki Nakanishi

    Physics letters B     page: 262   1991

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  47. Yang-Baxter eguation for the sl(n) chiral Potts model Reviewed

    Rinat Kashaev, Vladimir V. Mangazeev, Tomoki Nakanishi

    Nuclear Physics B     page: 362   1991

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  48. Ferro-and antiferro-magnetization in RSOS models Reviewed

    Atsuo Kuniba, Tomoki Nakanishi, Junji Suzuki

    Nuclear Physics B     page: 356   1991

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  49. 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

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    Language:English   Publishing type:Research paper (scientific journal)  

  50. Non-unitary minimal models and RSOSS MODELS Reviewed

    Tomoki Nakanishi

    Nuclear Physics B     page: 334   1990

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    Language:English  

  51. Radical root structure of conformal algebra Reviewed

    Tomoki Nakanishi

    Proyress of Theoutical Physice     page: 82   1989

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    Language:English  

  52. Differential equations in g>=2 conformal field theory Reviewed

    Akishi Kato, Tomoki Nakanishi

    Modern Physics letters A     page: 4   1989

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  53. Generalized Supersummrtry in Riemann surfaces and the associated string models Reviewed

    Tomoki Nakanishi

    Modern Physics letters A     page: 3   1988

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▼display all

Presentations 1

  1. 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 

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    Language:Japanese   Presentation type:Oral presentation (invited, special)  

KAKENHI (Grants-in-Aid for Scientific Research) 2

  1. 可積分系における新たな代数的組合せ論的構造の研究

    Grant number:16H03922  2016.4 - 2021.3

    科学研究費助成事業  基盤研究(B)

    中西 知樹, 国場 敦夫, 尾角 正人

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    Authorship:Principal investigator 

    Grant amount:\17940000 ( Direct Cost: \13800000 、 Indirect Cost:\4140000 )

    団代数の基礎に関する研究として、団パターンと散乱図式の関係に関する以下の研究を行なった。
    Fomin-Zelevinsky (2007)は団代数の背後にある代数的組み合わせ論的構造である団パターンに対する新しい手法を導入し、さまざまな予想を与えたが、中でも(1) C行列の符号同一性、(2) Laurent 正値性 (Laurent positivity)の二つが重要である。
    Gross-Hacking-Keel-Kontsevich (2018)は、この二つの予想を散乱図式の手法を用いて解決をした。この論文のプレプリントが出たのは2014年末であり、それ以来団代数理論の研究者に対する重要な文献となっている。一方、この論文は、上の二つの予想の証明も含め大変難解で、ごく一部の団代数理論のエキスパートにのみ理解されている状況が長らく続いてきた。したがって、この状況を改善し、より明解に団パターンと散乱図式との関係を明らかにし、また上の予想の証明を理解することは、私を含む団代数理論の研究者の課題であった。本研究では昨年までの準備を経て今年度本格的にこれに取り組み、その結果、Gross達の理論からトーリック幾何の設定を取り除き、純粋に散乱図式の構成定理だけに基づき、団パターンと散乱図式の関係を確立し、それを用いて上の二つの予想(定理)の証明を再構成することに成功をした。以上の結果を、論文としてまとめ2021年3月にarXivに投稿をした。
    Tomoki Nakanishi, Cluster patterns and scattering diagrams, arXiv:2103.16309, 70 pages.
    今年度は、昨年までの準備を経て、本研究課題の主要な課題の一つであった団パターンと散乱図式の関係の確立できた。要因としては、C行列の符号同一性と、団パターンにおけるG扇と散乱図式の壁との関係を正則木の距離に関する帰納法を用いて「同時に」示すことができることに気づいた点が最も重要であった。
    今年度の、団パターンと散乱図式の関係の確立の結果を踏まえて、次年度(最終年度)は、さらに一歩踏み込んで、散乱図式の構成における団変異から与えられる壁関数の役割を理解し、最終的には、散乱図式を取り除いた形でC行列の符号同一性の証明を与えることを目標とする。

  2. 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

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    Authorship:Principal investigator 

 

Teaching Experience (On-campus) 2

  1. Linear Algebra II

    2011

  2. Linear Algebra I

    2011