Integrable structures in mathematical physics and combinatorics
| Project/Area Number |
25400111
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Kindai University (2014-2017)
Kyoto University (2013) |
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Principal Investigator |
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| Research Collaborator |
NAKATSU Toshio
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| Project Period (FY) |
2013-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | melting crystal model / gauge theory / topological string / Young diagram / quantum torus algebra / quantum dilogarithm / quantum curve / integrable hierarchy / 溶解結晶模型 / Gromov-Witten不変量 / 位相的頂点 / Hurwitz数 / 双線形方程式 / KP階層 / 戸田階層 / Volterra階層 / 位相的弦理論 / 量子ミラー曲線 / 量子スペクトル曲線 / q-差分方程式 / τ函数 / Kac-Schwarz作用素 / フェルミオン / 量子トーラス代数 / 量子ダイログ函数 / 可積分階層 / オービフォルド / ミラー曲線 / コニフォールド / アブロビッツ・ラディック階層 |
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| Outline of Final Research Achievements |
The melting crystal model, 4D and 5D supersymmetric gauge theory and topological string theory on local toric Calabi-Yau manifolds have a common feature that the partition functions can be formulated in the language of Young diagrams.
We found that the KP hierarchy, the Toda hierarhy and their reductions underlie these models of mathematical physics and their variants. In the course of this research, new computational techniques based on the quantum torus algebra and the quantum diloarithmic functions were also developed. Moreover, we derived the quantum mirror (or spectral) curves associated with these models from the integrable structures, and pointed out that they are analogues of the Kac-Schwarz operators that have been known in the theory of integrable hierarchies.
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Report
(6 results)
Research Products
(22 results)
