2021 Fiscal Year Research-status Report
Localization formulae in Donaldson-Thomas theory of Calabi-Yau 4-folds
| Project/Area Number |
19K23397
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| Research Institution | Institute of Physical and Chemical Research |
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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 – 2023-03-31
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| Keywords | localization formulae / Donaldson-Thomas theory / Calabi-Yau 4-folds |
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| Outline of Annual Research Achievements |
In this academic year, I wrote two research papers: 1. "Gopakumar-Vafa type invariants of holomorphic symplectic 4-folds", 2. "Stable pairs and Gopakumar-Vafa type invariants on holomorphic symplectic 4-folds", jointly with Georg Oberdieck and Yukinobu Toda. We have submitted them to journals and they are now under referee process. Two of my previous written papers got published, one in "Mathematische Annalen" and one in "Advances in Mathematics". I was also invited to write a review paper "Yang-Mills theories on geometric spaces" published on "Reviews in Mathematical Physics". This seems to attract attentions of many researchers (over 15000 download according to the journal).
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| Current Status of Research Progress |
Current Status of Research Progress
3: Progress in research has been slightly delayed.
Reason
Due to COVID pandemic, my collaborators Sergej Monavari and Martijn Kool are not able to enter Japan to have face to face discussions. This makes a project on "crepant resolution conjecture of Calabi-Yau 4-folds" slightly delayed.
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| Strategy for Future Research Activity |
The border of Japan has reopened recently. Hopefully my collaborators mentioned above will be able to visit me in Japan later this year and we can then have face to face discussions and try to finish writing our ongoing joint papers.
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| Causes of Carryover |
Expect to use up all remaining funding in the coming fiscal year. It will be used to support travel expenses of my collaborator to visit me in Japan.
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