| Project/Area Number |
16H06337
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| Research Category |
Grant-in-Aid for Scientific Research (S)
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| Allocation Type | Single-year Grants |
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| Research Field |
Geometry
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| Research Institution | Osaka University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
藤野 修 大阪大学, 理学研究科, 教授 (60324711)
入谷 寛 京都大学, 理学研究科, 教授 (20448400)
小西 由紀子 津田塾大学, 学芸学部, 教授 (30505649)
安田 健彦 大阪大学, 理学研究科, 教授 (30507166)
岩木 耕平 東京大学, 大学院数理科学研究科, 准教授 (00750598)
神田 遼 大阪市立大学, 大学院理学研究科, 准教授 (50748324)
大川 新之介 大阪大学, 理学研究科, 准教授 (60646909)
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| Project Period (FY) |
2016-05-31 – 2021-03-31
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| Project Status |
Completed (Fiscal Year 2021)
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| Budget Amount *help |
¥103,870,000 (Direct Cost: ¥79,900,000、Indirect Cost: ¥23,970,000)
Fiscal Year 2020: ¥22,230,000 (Direct Cost: ¥17,100,000、Indirect Cost: ¥5,130,000)
Fiscal Year 2019: ¥22,750,000 (Direct Cost: ¥17,500,000、Indirect Cost: ¥5,250,000)
Fiscal Year 2018: ¥20,930,000 (Direct Cost: ¥16,100,000、Indirect Cost: ¥4,830,000)
Fiscal Year 2017: ¥20,020,000 (Direct Cost: ¥15,400,000、Indirect Cost: ¥4,620,000)
Fiscal Year 2016: ¥17,940,000 (Direct Cost: ¥13,800,000、Indirect Cost: ¥4,140,000)
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| Keywords | 代数学 / 幾何学 / 数理物理学 / ミラー対称性 / 双有理幾何学 |
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| Outline of Final Research Achievements |
By various research method (such as categorical entropy, semiorthogonal decompositions of derived categories, gamma integral structures and etc.), the fusion of the birational geometry and the theory of periods has been pushed forward and some great progress has been made towards solving important issues. By hiring post doctoral researchers, not only accelerating this research project itself, but it has laid the foundation for revitalization and future/sustainable development of the research field.
Research results are disseminated and external findings are acquired at many international conferences, workshops and study groups organized by this project, which encouraged and blossomed ideas that would lead to new research.
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| Academic Significance and Societal Importance of the Research Achievements |
理論物理学の背景に着想を得て新たな数学分野を開拓するだけでなく、双有理幾何学に対する新たな不変量や研究手法の提供を行い、また、離散群・特異点・ルート系・有限次元代数等の間にある不思議な関係のより深い理解を与えるなど、１００年以上の歴史がある数学の古典的・伝統的問題に対して新たな知見を加えた。
さらに、若手研究者との共同研究やスクールでの入門講義等を通じて、代々受け継がれた数学的伝統の次世代への継承を行った。
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| Assessment Rating |
Verification Result (Rating)
A+
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Assessment Rating |
Result (Rating)
A+: Progress in the research exceeds the initial goal. More than expected research results are expected.
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