| Project/Area Number |
22540186
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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 |
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| Co-Investigator(Renkei-kenkyūsha) |
SASAKI Ryu 京都大学, 基礎物理学研究所, 准教授 (20154007)
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| Project Period (FY) |
2010 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2010: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 代数解析 / 位相的弦理論 / 一般化コニフォールド / q差分方程式 / 量子ミラー曲線 / 溶解結晶模型 / 量子トーラス代数 / 戸田階層 / アブロビッツ・ラディック階層 / リーマン・ヒルベルト問題 / アブロヴィッツ・ラディック階層 / 無分散極限 / フロベニウス構造 / 準古典展開 / BD型可積分階層 / 一般化弦方程式 / フルヴィッツ数 / スペクトル曲線 / 一般化ホドグラフ法 / 対数的時間発展 |
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| Research Abstract |
Integrable hierarchies are a class of classical integrable system. Typical examples are the KP hierarchy, the Toda hierarchy and multi-component versions thereof. This research is focussed on both theoretical aspects and applications to mathematical physics. All materials play an important role in recent progress of mathematical physics. As regards the theoretical aspect, we have obtained some results on the Toda hierarchy, the dispersionless Toda hierarchy and integrable hierarchies of the B and D types. Subjects of applications to mathematical physics range over statistical mechanics, gauge theories, string theories and related mathematical issues. Solvable models in discrete quantum mechanics are also studied in the context of orthogonal polynomials.
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