| Project/Area Number |
16340040
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 University, Graduate School of Human and Environmental Studies, Professor, 人間・環境学研究科, 教授 (40171433)
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| Co-Investigator(Kenkyū-buntansha) |
IKEDA Takeshi Science University of Okayama, Faculty of Science, Lecturer, 理学部, 講師 (40309539)
SASAKI Ryu Kyoto University, Yukawa Institute, Associate Professor, 基礎物理学研究所, 助教授 (20154007)
SHIMIZU Yuji International Christian University, Division of Natural Sciences, Associate Professor, 教養学部, 準教授 (80187468)
TAKEBE Takashi Ochanomizu University, Faculty of Science, Associate Professor, 理学部, 助教授 (60240727)
FUJII Michihiko Kyoto University, Faculty of Science, Associate Professor, 理学研究科, 助教授 (60254231)
塩田 隆比呂 京都大学, 大学院・理学研究科, 助教授 (20243008)
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| Project Period (FY) |
2004 – 2006
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| Project Status |
Completed (Fiscal Year 2006)
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| Budget Amount *help |
¥8,800,000 (Direct Cost: ¥8,800,000)
Fiscal Year 2006: ¥2,500,000 (Direct Cost: ¥2,500,000)
Fiscal Year 2005: ¥3,000,000 (Direct Cost: ¥3,000,000)
Fiscal Year 2004: ¥3,300,000 (Direct Cost: ¥3,300,000)
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| Keywords | integrable hierarchy / dispersionless integrable system / solvable many body system / gauge theory / free fermion / conformal mapping / Grassmann manifold / hyperbolic structure / 量子可積分系 / 無分散極限 / ランダム行列 / 等モノドロミー変形 / ハミルトン構造 / 同変コホモロジー / Calogero系 / Loewner方程式 / 共形写像 / 広田方程式 / ソリトン方程式 / 共形場理論 / q類似 / 楕円類似 / インスタントン |
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| Research Abstract |
1.We considered the instanton sum of four and five dimensional supersymmetric gauge theories as a model of random (plane) partitions, and applied the method of free fermions for integrable hierarchies to derive the Seiberg-Witten curve.
2.We pointed out a relation between a special class of deformation process of conformal mapping and a kind of dispersionless integrable systems. A solution technique (hodograph method) of such integrable systems was also studied.
3.We derived several new dispersionless integrable systems.as quasi-classical limit from integrable hierarchies. An example is related to a q-analogue of the modified KP (and Toda) hierarchy. Another example is obtained from the two-component BKP hierarchy. Moreover, we could identify the so called genus-zero universal Whitham hierarchy to be quasi-classical limit of a multi-component analogue of the KP hierarchy.
4.We elucidated some new features of solvable many body systems (the Calogero-Moser system, the Sutherland systems, and their variants) such as : equilibrium configuration, shape invariance, creation-annihilation operator (as quantum mechanics), direct integration method (as classical mechanics), etc.
5.We obtained several geometric results on Grassmann manifolds, noncommutative algebraic varieties, invariants of low dimensional manifolds, hypergeometric equations related to hyperbolic cones, etc.
6.We did some other researches on random matrices, Seiberg-Witten integrable systems, isomonodromic deformations, integrable systems related to a moduli space of vector bundles, etc.
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