| Project/Area Number |
18K03304
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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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| Review Section |
Basic Section 11020:Geometry-related
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| Research Institution | Kyushu University |
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Principal Investigator |
Kaji Shizuo 九州大学, マス・フォア・インダストリ研究所, 教授 (00509656)
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| Project Period (FY) |
2018-04-01 – 2023-03-31
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| Project Status |
Completed (Fiscal Year 2022)
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| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2022: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2021: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2020: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 同変トポロジー / 計算トポロジー / ワイル群 / 旗多様体 / コンパクトリー群 / 有限群のコホモロジー / 実トーリック多様体 / パーシステントホモロジー / 位相幾何学 |
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| Outline of Final Research Achievements |
The most interesting result obtained during the research period is the determination of the action of the Weil group on the cohomology of the real toric manifolds associated with root systems. As a byproduct, a topological realisation of a combinatorial object known as the generalised Euler's zigzag numbers were obtained.
Throughout the research period, a number of algorithms for computing concrete examples regarding flag manifolds, real toric manifolds, and Weyl groups were developed.
Also, computer programmes were produced and made publicly available as open-source software, and they have been used in various fields outside of mathematics.
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| Academic Significance and Societal Importance of the Research Achievements |
旗多様体や実トーリック多様体といった空間のトポロジーと組合せ論を協調させて解析する実例を複数提供したことが，同変トポロジー分野における学術的意義といえる．
また，計算アルゴリズムを開発しその実装を公開したことで，今後具体例から新たな知見が得られることが期待される．
応用として，機械学習や画像解析の手法を開発し，こちらもその実装を公開している．実際に医療・材料・データ解析などに利用されており，社会還元がなされている．
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