| Project/Area Number |
24K06666
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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 11010:Algebra-related
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| Research Institution | Nagoya University |
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Principal Investigator |
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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| Project Period (FY) |
2024-04-01 – 2029-03-31
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| Project Status |
Granted (Fiscal Year 2024)
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| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2028: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2027: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2026: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2025: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2024: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | representation theory / homological algebra / quiver representation / cluster structure / topological surfaces |
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| Outline of Research at the Start |
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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| Outline of Annual Research Achievements |
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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| Current Status of Research Progress |
Current Status of Research Progress
3: Progress in research has been slightly delayed.
Reason
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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| Strategy for Future Research Activity |
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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