| 研究課題/領域番号 |
24K06666
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| 研究種目 |
基盤研究(C)
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| 配分区分 | 基金 |
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| 応募区分 | 一般 |
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| 審査区分 |
小区分11010:代数学関連
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| 研究機関 | 名古屋大学 |
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研究代表者 |
チャン アーロンケイヤム 名古屋大学, 多元数理科学研究科, 助教 (50845039)
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| 研究期間 (年度) |
2024-04-01 – 2029-03-31
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| 研究課題ステータス |
交付 (2024年度)
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| 配分額 *注記 |
4,550千円 (直接経費: 3,500千円、間接経費: 1,050千円)
2028年度: 910千円 (直接経費: 700千円、間接経費: 210千円)
2027年度: 910千円 (直接経費: 700千円、間接経費: 210千円)
2026年度: 910千円 (直接経費: 700千円、間接経費: 210千円)
2025年度: 910千円 (直接経費: 700千円、間接経費: 210千円)
2024年度: 910千円 (直接経費: 700千円、間接経費: 210千円)
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| キーワード | representation theory / homological algebra / quiver representation / cluster structure / topological surfaces |
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| 研究開始時の研究の概要 |
Cluster algebras are mathematical structures generated by variables that can change in specific ways. Our interest is in those that arise from the study of geometry of topological surfaces. Our aim is to study this by expanding some of the current algebraic methods called categorification.
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| 研究実績の概要 |
I have finished one full project with my collaborators on total preprojective algebra. The preprint is now available on arXiv. We explored various properties of it that mimic the classica preprojective algebras.
Several submissions in the previous years are still waiting for review. But at least one of them (study on periodic trivial extension algebras) is fully accepted and is waiting for the actual publication.
Towards the end of the year, I have also visited Bonn and spent some time intensively conducting research with my long-term collaborator. This is related to the total preprojective algebra mentioned above. We explored similar construction and investigate possible new approach in categorification of cluster algebras.
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| 現在までの達成度 |
現在までの達成度
3: やや遅れている
理由
I have been juggling between several projects. One is completely done and one is close to finish, several are still in progress. Unfortunately none of these was close to the theme proposed in the Grant-in-Aid research project; nevertheless, the time spent on these other projects will be meaningful as all projects are inter-related.
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| 今後の研究の推進方策 |
Another foreign research visit is in the planning. One project in progress is close to finish; another one has seen significant progress and maybe ready for proper write-up in a few months time. After that I would like to spent time focus back on representation theory of gentle algebras and surface topology, as proposed in the original Grant-in-Aid applications.
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