| Project/Area Number |
23K03030
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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 |
BACHMANN Henrik 名古屋大学, 多元数理科学研究科, 准教授 (20813372)
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| Project Period (FY) |
2023-04-01 – 2026-03-31
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| Project Status |
Granted (Fiscal Year 2023)
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| Budget Amount *help |
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2025: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2024: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2023: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | multiple zeta values / Eisenstein series / modular forms / q-analogues of MZV |
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| Outline of Research at the Start |
This research projects deals with the modular phenomena for finite multiple zeta values. This project is motivated by the Kaneko-Zagier which predicts an explicit connection of classical multiple zeta values, for which some modular phenomena can be explained, and their finite analogues.
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| Outline of Annual Research Achievements |
In this year, I finished the project "Formal multiple Eisenstein series and their derivations" in joint work with Jan-Willem van Ittersum. In this work we introduce formal multiple Eisenstein series as a formal analogue for multiple Eisenstein series. This can be seen as a natural analog of formal multiple zeta values, which are constructed as formal symbols satisfying the extended double shuffle relations. The main result of this project is that we show that the algebra of formal multiple Eisenstein series as the structure of an sl2-algebra, generalizing the sl2-structure of quasimodular forms in a natural way. Besides this, I started another project on formal finite multiple zeta values and on the algebraic structure of certain q-analogues.
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| Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
The work on formal multiple Eisenstein series was finally finished positively after almost 3 years. It was presented by me at several conferences abroad and also domestically.
The new project on formal finite multiple zeta values is going smoothly, and me and my collaborator (Risan, Nagoya University) have already obtained several new results. We still have a lot of open questions we want to address, but are doing steady progress on them.
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| Strategy for Future Research Activity |
Besides the above-mentioned projects, I am currently also discussing a possible further project with Tadashi Okazaki on the connection to physics. Besides this I am planning to give several talks this year on the ongoing projects on formal finite multiple zeta values. The first one will be at a conference in China in June. In the summer, I am planning to organize a mini workshop on q-analogs of multiple zeta values in Hamburg, Germany. There, I will also meet some of my former collaborators to discuss further possible projects.
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