| Project/Area Number |
19K23397
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Multi-year Fund |
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| Review Section |
0201:Algebra, geometry, analysis, applied mathematics,and related fields
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| Research Institution | Institute of Physical and Chemical Research (2021-2022)
The University of Tokyo (2019-2020) |
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Principal Investigator |
Cao Yalong 国立研究開発法人理化学研究所, 数理創造プログラム, 研究員 (80791459)
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| Project Period (FY) |
2019-08-30 – 2024-03-31
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| Project Status |
Granted (Fiscal Year 2022)
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| Budget Amount *help |
¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2020: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2019: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | Curve counting / Calabi-Yau 4-folds / crepant resolution / localization formulae / Donaldson-Thomas theory |
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| Outline of Research at the Start |
In 2013-2015, the applicant with Leung and Borisov with Joyce made progress on the theory of Donaldson-Thomas invariants on Calabi-Yau 4-folds. Computations of such invariants are in general very difficult. The proposal aims to develop localization formulae to effectively compute such invariants when there are torus actions on the corresponding moduli spaces. In particular, we aim to compute DT4 invariants for: (1) moduli spaces of stable pairs, (2) Hilbert schemes.
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| Outline of Annual Research Achievements |
In this year, I wrote one paper "A Donaldson-Thomas crepant resolution conjecture on Calabi-Yau 4-folds" with Martijn Kool (from Utrecht University) and Sergej Monavari (from Ecole Polytechnique Federale de Lausanne). We have submitted it to a journal for referee. I have also been working with Gufang Zhao from Melbourne university on quasimap theory to quivers with potentials. The paper will appear soon.
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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
I have kept discussions with my collaborators via email communications and zoom meetings. This enables us to finish our project smoothly.
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| Strategy for Future Research Activity |
My collaborators will visit me in Japan later this year and we can then have face to face discussions and decide the future projects.
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