団代数の基礎と応用の研究

2015 Fiscal Year Annual Research Report

• Project/Area Number: 23540012
• Research Institution: Nagoya University
• Principal Investigator: 中西 知樹 名古屋大学, 多元数理科学研究科, 教授 (80227842)
• Project Period (FY): 2011-04-28 – 2016-03-31
• Keywords: 団代数 / ダイログ関数

Outline of Annual Research Achievements

今年度は引き続き団代数の基礎と応用の研究を行った。具体的には１。一般団代数の研究、特に高次ダイログ関数の関数等式の導出、２。Gross等による散乱図形による交換図の記述を用いた団代数の研究、３。団代数の亜群による定式化、などの研究を行い、さまざまな成果が得られた。研究成果の一部について論文[1]を公表し、また一部については現在論文を執筆中である。

[1] Tomoki Nakanishi, Dylan Rupel, Companion cluster algebras to a generalized cluster algebra, to appear in Travaux Mathematiques, arXiv:1504.06758, 14 pages.

Research Products

• [Int'l Joint Research] Northeastern University(米国)
  • Country Name: U.S.A.
  • Counterpart Institution: Northeastern University
• [Journal Article] Exact WKB analysis and cluster algebras II: simple poles, orbifold points, and generalized cluster algebras (2015)
  • Author(s): Kohei Iwaki, Tomoki Nakanishi
  • Journal Title: Int. Math. Res. Not. Volume: online first Pages: ー
  • DOI: DOI 10.1093/imrn/rnv270
  • Peer Reviewed / Open Access
• [Journal Article] Structure of seeds in generalized cluster algebras (2015)
  • Author(s): Tomoki Nakanishi
  • Journal Title: Pacific J. Math. Volume: 277 Pages: 201,218
  • DOI: DOI:10.2140/pjm.2015.277.201
  • Peer Reviewed / Open Access
• [Journal Article] Quantum generalized cluster algebras and quantum dilogarithms of higher degrees (2015)
  • Author(s): Tomoki Nakanishi
  • Journal Title: Theor. Math. Phys. Volume: 185 Pages: 1759,1768
  • DOI: DOI:10.1007/s11232-015-0377-9
  • Peer Reviewed / Open Access
• [Presentation] Introduction to cluster algebras および Tropical variables in cluster algebras （計２講演） (2016)
  • Author(s): Tomoki Nakanishi
  • Organizer: Tropical Geometry and Related Topic
  • Place of Presentation: 京都大
  • Year and Date: 2016-03-07 – 2016-03-11
  • Int'l Joint Research / Invited
• [Presentation] Introduction to cluster algebras (2015)
  • Author(s): Tomoki Nakanishi
  • Organizer: Symposium on Representation Theory 2015
  • Place of Presentation: 伊豆長岡
  • Year and Date: 2015-11-17 – 2015-11-20
  • Int'l Joint Research / Invited
• [Presentation] Riemann surface and cluster algebra (2015)
  • Author(s): Tomoki Nakanishi
  • Organizer: Quantization of Spectral Curves
  • Place of Presentation: 大阪市大
  • Year and Date: 2015-11-02 – 2015-11-06
  • Int'l Joint Research / Invited
• [Presentation] Cluster algebras and applications (2015)
  • Author(s): Tomoki Nakanishi
  • Organizer: School and International Conference on Geometry and Quantization GEOQUANT 2015
  • Place of Presentation: ICMAT, Madrid, Spain
  • Year and Date: 2015-09-07 – 2015-09-18
  • Int'l Joint Research / Invited
• [Presentation] On generalized cluster algebras (2015)
  • Author(s): Tomoki Nakanishi
  • Organizer: The Ninth IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory
  • Place of Presentation: University of Georgia, Atlanta, USA
  • Year and Date: 2015-04-01 – 2015-04-04
  • Int'l Joint Research / Invited
• [Remarks]
  • URL: http://www.math.nagoya-u.ac.jp/~nakanisi/index.html