| 研究課題/領域番号 |
19K23397
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| 研究種目 |
研究活動スタート支援
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| 配分区分 | 基金 |
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| 審査区分 |
0201:代数学、幾何学、解析学、応用数学およびその関連分野
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| 研究機関 | 国立研究開発法人理化学研究所 (2021-2022)
東京大学 (2019-2020) |
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研究代表者 |
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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| 研究期間 (年度) |
2019-08-30 – 2024-03-31
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| 研究課題ステータス |
交付 (2022年度)
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| 配分額 *注記 |
2,470千円 (直接経費: 1,900千円、間接経費: 570千円)
2020年度: 1,300千円 (直接経費: 1,000千円、間接経費: 300千円)
2019年度: 1,170千円 (直接経費: 900千円、間接経費: 270千円)
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| キーワード | Curve counting / Calabi-Yau 4-folds / crepant resolution / localization formulae / Donaldson-Thomas theory |
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| 研究開始時の研究の概要 |
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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| 研究実績の概要 |
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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| 現在までの達成度 (区分) |
現在までの達成度 (区分)
2: おおむね順調に進展している
理由
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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| 今後の研究の推進方策 |
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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