2023 Fiscal Year Final Research Report
Transversal Study of Quandles, Symmetric Spaces, and Combinatorics
Project/Area Number |
19K21831
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Research Category |
Grant-in-Aid for Challenging Research (Exploratory)
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Allocation Type | Multi-year Fund |
Review Section |
Medium-sized Section 11:Algebra, geometry, and related fields
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Research Institution | Osaka Metropolitan University (2022-2023) Osaka City University (2019-2021) |
Principal Investigator |
Tamaru Hiroshi 大阪公立大学, 大学院理学研究科, 教授 (50306982)
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Project Period (FY) |
2019-06-28 – 2024-03-31
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Keywords | カンドル / 対称空間 / グラフ / 組み合わせ論 |
Outline of Final Research Achievements |
We have made progress in the transversal study of quandles, symmetric spaces, and combinatorics. We published a paper that newly formulates the concept of s-commutative subsets for quandles. This concept is closely related to combinatorics and coding theory, and is also an extension of antipodal sets studied in the theory of symmetric spaces. Additionally, the new method of constructing quandles obtained by observing symmetric spaces utilizes graphs, which is another outcome of our transversal research. Furthermore, we oeganized an annual conference titled "Quandles and Symmetric Spaces" every year, and an overview paper is scheduled to be published in the journal "Sugaku" issued by the Mathematical Society of Japan. We believe this contributes to the advancement of new research and the fostering of future researchers.
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Free Research Field |
幾何学
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Academic Significance and Societal Importance of the Research Achievements |
我々の研究成果は,カンドルの研究を中心として,対称空間論および組み合わせ論などの様々な分野と関係する新たな研究領域を開拓するものと自負している。これにより,カンドルの研究に新しい道具や概念を持ち込み,さらに対称空間論などの既存の研究分野にも新しい問題意識を持ち込んでおり,その学術的意義は大きいと考える。また,研究代表者と大学院生等の若手研究者の共同研究も多く,さらに我々の研究成果に触発されて他大学の大学院生が新たな研究成果を得るなどの成果もある。このように我々の研究成果は,多くの教育的効果を上げており,若手研究者育成にも寄与していると考える。
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