| Project/Area Number |
23K12983
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| Research Category |
Grant-in-Aid for Early-Career Scientists
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| Allocation Type | Multi-year Fund |
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| Review Section |
Basic Section 12010:Basic analysis-related
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| Research Institution | Hokkaido University |
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Principal Investigator |
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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 |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2025: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2024: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2023: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
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| Keywords | Schubert calculus / TASEP / integrable system / Grothendieck polynomial / boson-fermion relation / Lie superalgebra |
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| Outline of Research at the Start |
We will expand upon a recent connection found between probability theory, geometry, and mathematical physics. We will examine the class of half-space particle systems and its relationship with the K-theory rings of the Lagrangian and orthogonal Grassmannian.
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| Outline of Annual Research Achievements |
Posted the preprint (arXiv: 2311.01116) that provided the main link for this project. Gave presentations at multiple international conferences and seminars in America, India, France, Germany, Australia, and Spain about results related to this project. Visited international researchers in France, Sweden, Austria, Australia, Germany, Spain, South Korea, and America -- as well as domestic researchers in Tokyo, Osaka, and Kyoto -- to discuss research related to this project. A number of these discussions are expected to lead to further preprints appearing in FY2024 that will result in publications in top-tier international journals. Hosted international visitors to have discussions and to give seminars related to this project.
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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 results in this project are being produced at the expected rate due to the ability to have meetings with various researchers in Japan and internationally. In addition, there are further forthcoming results related to this project that were not initially expected and are currently being developed. It is not expected that completing these complementary results will have a major impact on the timeline of achieving the main goal of this project.
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| Strategy for Future Research Activity |
This upcoming year, I will be part of the organizing committee of a large international conference (over 200 participants). As part of this conference, I will interact with numerous researchers to discuss aspects of this project. I expect to produce at least 4 preprints in FY2024 related to this project, which I will then disseminate the results at conferences and seminars. By doing so, further results and connections can be made, which will further enhance the outcomes of this project. There are currently no plans to change the research plan.
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