Exact WKB analysis, cluster algebras and topological recursion
| Project/Area Number |
16K17613
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Basic analysis
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| Research Institution | The University of Tokyo (2020)
Nagoya University (2016-2019) |
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Principal Investigator |
Iwaki Kohei 東京大学, 大学院数理科学研究科, 准教授 (00750598)
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| Project Period (FY) |
2016-04-01 – 2021-03-31
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| Project Status |
Completed (Fiscal Year 2020)
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| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2019: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2018: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 完全WKB解析 / 位相的漸化式 / Painleve方程式 / 団代数 / BPS構造 / Voros係数 / 量子曲線 / パンルヴェ方程式 |
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| Outline of Final Research Achievements |
We investigated a relationship between exact WKB analysis, cluster algebras, and topological recursion. The results we obtained are the following: (1) We proved that the discrete Fourier transform of topological recursion partition function gives a Painleve tau-function. (2) For a class spectral curves, we established a formula which allows us to describe the free energy of topological recursion in terms of the corresponding BPS structure.
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| Academic Significance and Societal Importance of the Research Achievements |
微分方程式論の研究手法である完全WKB解析と、代数学の研究対象である団代数やBPS構造、さらには幾何学や数理物理学と密接に関わる位相的漸化式との関係性に関する研究を行ったことで、全く異なる分野の知見を共有する足掛かりを与えることができた。これが本研究成果の学術的意義である。
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Report
(6 results)
Research Products
(52 results)
