| Project/Area Number |
19540179
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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 University, 大学院・人間・環境学研究科, 教授 (40171433)
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| Co-Investigator(Kenkyū-buntansha) |
SASAKI Ryu 京都大学, 基礎物理学研究所, 准教授 (20154007)
TAKEBE Takashi お茶の水女子大学, 理学部, 准教授 (60240727)
IKEDA Takeshi 岡山理科大学, 理学部, 講師 (40309539)
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| Project Period (FY) |
2007 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2007: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 可積分系 / 無分散可積分系 / フェイ型等式 / ランダム平面分割 / 量子トーラス代数 / 対数的時間発展 / 等角写像 / 準古典展開 / KP階層 / 戸田階層 / 普遍Whitham階層 / Ablowitz-Ladik階層 / 一般化弦方程式 / 溶解結晶模型 / 流体力学的簡約 / 無分散広田方程式 / 超対称ゲージ理論 / Pfaff-戸田階層 / Fay型等式 / 可積分階層 / インスタントン和 |
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| Research Abstract |
"Integrable systems" is a collective name for "solvable" mathematical models. They are mostly a differential equation, but some cases are formulated as a probability distribution or a stochastic process. Integrable systems are interesting not only because they can be solved by a systematic method, but also remarkable for rich mathematical structures hidden behind. In this research project, we sought for new material in mathematical physics after 2000, and obtained several results on integrable systems themselves and on their applications to gauge theory and string theory. These results are expected to lead to new research.
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