I am currently an associate professor at the Morningside Center of Mathematics, Chinese Academy of Sciences. I am doing research on algebraic geometry, symplectic geometry and mathematical physics with special emphasis on higher dimensional gauge theory. I have been studying Donaldson-Thomas type theory on Calabi-Yau 4-folds, which is a way to count instantons and coherent sheaves on CY4.
Papers and preprints
1. Quasimaps to quivers with potentials, (with G. Zhao). arXiv:2306.01302.
2. A Donaldson-Thomas crepant resolution conjecture on Calabi-Yau 4-folds, (with M. Kool and S. Monavari). Transactions of the American Mathematical Society, 376 (2023), no. 11, 8225-8268. arXiv:2301.11629.
3. Stable pairs and Gopakumar-Vafa type invariants on holomorphic symplectic 4-folds, (with G. Oberdieck and Y. Toda). Advances in Mathematics, 408 (2022) 108605, 44 pages. arXiv: 2201.11540.
4. Gopakumar-Vafa type invariants of holomorphic symplectic 4-folds, (with G. Oberdieck and Y. Toda). To appear in Communications in Mathematical Physics. arXiv:2201.10878.
5. Yang-Mills theories on geometric spaces. Reviews in Mathematical Physics, 34 (2022), no. 1, Paper No. 2230001, 18 pp.
6. Tautological Hilbert scheme invariants of Calabi-Yau 4-folds via virtual pullback, (with F. Qu). arXiv:2012.04415.
7. Counting perverse coherent systems on Calabi-Yau 4-folds, (with Y. Toda). Mathematische Annalen 385 (2023), no. 3-4, 1-51. arXiv:2009.10909.
8. Tautological stable pair invariants of Calabi-Yau 4-folds, (with Y. Toda). Advances in Mathematics 396 (2022) 108176, 44 pages. arXiv:2009.03553.
9. Stable pair invariants of local Calabi-Yau 4-folds, (with M. Kool and S. Monavari). International Mathematics Research Notices 2022, no. 6, 4753-4798. arXiv:2004.09355.
10. Gopakumar-Vafa type invariants on Calabi-Yau 4-folds via descendent insertions, (with Y. Toda). Communications in Mathematical Physics, 383 (2021), no. 1, 281-310. arXiv:2003.00787.
11. Curve counting via stable objects in derived categories of Calabi-Yau 4-folds, (with Y. Toda). Advances in Mathematics, 406 (2022) 108531, 58 pages. arXiv:1909.04897.
12. K-theoretic DT/PT correspondence for toric Calabi-Yau 4-folds, (with M. Kool and S. Monavari). Communications in Mathematical Physics, 396 (2022), no. 1, 225–264. arXiv:1906.07856.
13. Curve counting and DT/PT correspondence for Calabi-Yau 4-folds, (with M. Kool). Advances in Mathematics, 375 (2020) 107371, 49 pages. arXiv:1903.12171.
14. Stable pairs and Gopakumar-Vafa type invariants for Calabi-Yau 4-folds, (with D. Maulik and Y. Toda). Journal of the European Mathematical Society 24 (2022), no. 2, 527-581. arXiv:1902.00003.
15. Orientability of moduli spaces of Spin(7)-instantons and coherent sheaves on Calabi-Yau 4-folds, (with J. Gross, D. Joyce). Advances in Mathematics, 368 (2020) 107134, 60 pages. arXiv:1811.09658, v2.
16. Curve counting on An×C2. Pure and Applied Mathematics Quarterly (Special Issue in Honor of Prof. Kyoji Saito’s 75th Birthday), vol. 16, No. 3 (2020), pp. 659-674.
17. Counting zero-dimensional subschemes in higher dimensions, (with M. Kool). Journal of Geometry and Physics, 136 (2019) 119-137. arXiv:1805.04746.
18. Counting conics on sextic 4-folds. Mathematical Research Letters, 26 (2019), no. 5, 1343-1357. arXiv:1805.04696.
19. Genus zero Gopakumar-Vafa type invariants for Calabi-Yau 4-folds II: Fano 3-folds. Communications in Contemporary Mathematics, 22 (2020), no. 7, 1950060, 25 pages. arXiv:1801.06130.
20. Genus zero Gopakumar-Vafa type invariants for Calabi-Yau 4-folds, (with D. Maulik and Y. Toda). Advances in Mathematics, 338 (2018), 41-92. arXiv:1801.02513.
21. Zero dimensional Donaldson-Thomas invariants of Calabi-Yau 4-folds, (with M. Kool). Advances in Mathematics, 338 (2018), 601-648. arXiv:1712.07347.
22. Remarks on Kawamata's effective non-vanishing conjecture for manifolds with trivial first Chern classes, (with C. Jiang). Mathematische Zeitschrift, 296 (2020), 615-637. arXiv:1612.00184.
23. Mukai flops and Plucker type formulas for hyper-Kahler manifolds, (with N. C. Leung). Proceedings of the American Mathematical Society, 148 (2020), no. 10, 4119- 4135. arXiv:1510.05889.
24. Remarks on mirror symmetry of Donaldson-Thomas theory for Calabi-Yau 4-folds, (with N. C. Leung). "Tsinghua Lectures in Mathematics", Adv. Lect. Math. 45, (2018), Higher Education Press. arXiv:1506.04218.
25. Relative Donaldson-Thomas theory for Calabi-Yau 4-folds, (with N. C. Leung). Transactions of the American Mathematical Society, 369 (2017), 6631- 6659. arXiv:1502.04417.
26. Orientability for gauge theories on Calabi-Yau manifolds, (with N. C. Leung). Advances in Mathematics, 314 (2017), 48-70. arXiv:1502.01141.
27. Donaldson-Thomas theory for Calabi-Yau 4-folds, (with N. C. Leung). arXiv:1407.7659.
Education
1. B.Eng. Tsinghua University, 2007-2011.
2. M.S. The Chinese University of Hong Kong, 2011-2013. Thesis advisor: Naichung Conan Leung
3. Ph.D. The Chinese University of Hong Kong, 2013-2016. Thesis advisor: Naichung Conan Leung
Employment
1. August 2016-April 2017, Project Researcher, Kavli IPMU, The University of Tokyo, Japan
2. April 2017-March 2019, Royal Society Newton International Fellow, affiliated at University of Oxford
3. March 2019-July 2021, Project Researcher, Kavli IPMU, The University of Tokyo, Japan
4. July 2021- April 2023, Research Scientist, RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program, Japan
5. April 2023-January 2024, Senior Research Scientist, RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program, Japan
6. January 2024-now, Associate Professor, Morningside Center of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, China
