| Project/Area Number |
10640165
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | KYOTO UNIVERSITY |
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Principal Investigator |
TAKASAKI Kanehisa Kyoto Univ, Integrated Human Studies, Ass, Professor, 総合人間学部, 助教授 (40171433)
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| Co-Investigator(Kenkyū-buntansha) |
SAKURAGAWA Takashi Kyoto Univ, Integrated Human Studies, Ass, Professor, 総合人間学部, 助教授 (60196136)
VEDA Tetsuo Kyoto Univ, Integrated Human Studies, Professor, 総合人間学部, 教授 (10127053)
UE Masaaki Kyoto Univ, Integrated Human Studies, Ass, Professor, 総合人間学部, 助教授 (80134443)
USHIKI Shigehiro Kyoto Univ, Graduate School of Human and Environmental Studies, Professor, 大学院・人間・環境学研究科, 教授 (10093197)
HATA Masayoshi Kyoto Univ, Integrated Human Studies, Ass, Professor, 総合人間学部, 助教授 (40156336)
西山 享 京都大学, 総合人間学部, 助教授 (70183085)
松木 敏彦 京都大学, 総合人間学部, 助教授 (20157283)
加藤 信一 京都大学, 総合人間学部, 助教授 (90114438)
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| Project Period (FY) |
1998 – 1999
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| Project Status |
Completed (Fiscal Year 1999)
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| Budget Amount *help |
¥3,300,000 (Direct Cost: ¥3,300,000)
Fiscal Year 1999: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 1998: ¥2,100,000 (Direct Cost: ¥2,100,000)
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| Keywords | integrable system / Whitham deformation / isomonodromic deformation / supersymmetric field theory / topological field theory / solvable spin system / conformal field theory / Toda lattice / 共形場理論 / モノドロミー保存変形 / 有限次元可積分系 / 超対称性 / ゲージ理論 / 位相不変量 / 表現論 / 複素力学系 / セルオートマトン |
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| Research Abstract |
This research project aimed to search for various finite dimensional integrable systems in systems with infinite degrees of freedom, and to elucidate their mathematical structures. Related issues on geometry and non-integrable systems were also investigated.
The head investigator obtained interesting results on Whitham deformation equations, isomonodromic deformations, systems arising in supersymmetric/topological gauge theories and Calogero-Moser systems, all of which are mutually related. Firsly, he could find an explicit form of the Whitham deformation equations for asymptoci description of isomonodromic systems on the Rie-mann sphere. Secondly, an extension, to a torus, of such isomonodromic systems was achieved on the basis of methods in solvable spin sysmtes and conformal field theories. Thirdly, he clarified the roles that the tau functions and the Whitham deformations play in four dimensional supersymmetric and topolotical gauge theories. Finally, he considered the elliptic Calogero-Moser systems, which are also closely related to four dimensional supersymmetric gauge theories, and discoveref that a non-autonomous analogues of those systems give an example of isomonodromic dermations on a torus.
The achievement due to other members of the project group respectively ranges over low-dimensional topology, stochastic analysis of hypoelliptic operators, complex dynamical systems, transcendental number theory related to nonlinear dynamical systems, celular automata, intelligent agents, hypoelliptic and hyperbolic equations with infnite degeneracy,
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