| Project/Area Number |
26800072
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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 |
Mathematical analysis
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| Research Institution | Josai University |
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Principal Investigator |
Hiroe Kazuki 城西大学, 理学部, 助教 (50648300)
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| Research Collaborator |
OSHIMA Toshio 城西大学, 理学部数学科, 教授 (50011721)
YAMAKAWA Daisuke 東京理科大学, 理学部第一部数学科, 講師 (20595847)
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 不確定特異点 / ワイル群 / ミドル・コンボリューション / 箙の表現論 / Stokes現象 / 結び目 / スペクトル曲線 / ストークス現象 / 平面代数曲線の特異点 / 絡み目 / モノドロミー保存変形 / 微分方程式の不確定特異点 / 箙多様体 / Kac-Moody Lie環 / 代数曲線の特異点 |
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| Outline of Final Research Achievements |
I gave an isomorphism between a moduli space of algebraic differential equations on the Riemann sphere and quiver variety as symplectic manifolds when differential equations have at most one unramified irregular singular point. When the differential equations have arbitrary number of unramified irregular singular points, although it was known that the moduli space can not be isomorphic to any quiver varieties, I constructed an open embedding into a quiver variety which is not surjective in general and clarified a relation between middle convolution of differential equations and Wely group of the quiver, also determined a necessary and sufficient conditon to the nonemptiness of the regular part of the moduli space.
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