研究领域
My research interests lie in the intersection between algebras, topology and geometry, with motivation coming from mathematical physics, e.g. (homological) mirror symmetry. In particular, I study things like Bridgeland’s stability conditions on triangulated categories, quivers with superpotentials, Calabi-Yau/Fukaya categories, braid groups, cluster theory, quadratic differentials, etc.
教育背景
2008-2011 博士 巴斯大学 (Uni. of Bath, UK)
2004-2008 学士 北京大学
工作经历
2020至今 清华大学丘成桐数学科学中心 教授
2018-2020 清华大学丘成桐数学科学中心 副教授
2016-2020 香港中文大学 研究助理教授
2013-2016 挪威科技大学 博士后
2012-2012 加拿大主教大学 博士后
荣誉与奖励
2016 国际代数表示论会议(ICRA)奖
发表论文
1. On the focus order of planar polynomial differential equations, with J. Yang,
J. Diff. Equations, 246 (2009), pp 3361-3379.
2. Ext-quivers of hearts of A-type and the orientation of associahedron,
J. Algebra, 393 (2013), pp 60-70. (arXiv:1202.6325)
3. Exchange graphs and Ext quivers, with A. King,
Adv. Math. 285 (2015), pp 1106–1154. (arXiv:1109.2924).
4. Stability conditions and quantum dilogarithm identities for Dynkin quivers,
Adv. Math. 269 (2015), pp 220-264. (arXiv:1111.1010)
5. Tagged mapping class group: Auslander-Reiten translations, with T. Brustle,
Math. Zeit. 279 (2015), pp 1103-1120. (arXiv:1212.0007)
6. C-sortable words as green mutation sequences,
Proc. Lond. Math. Soc. 111 (2015), pp 1052-1070. ( arXiv:1205.0034)
7. Decorated marked surfaces: Spherical twists versus braid twists,
Math. Ann. 365 (2016), pp 595-633.(arXiv:1407.0806).
8. Cluster categories for marked surfaces: punctured case, with Y. Zhou,
Compos. Math. 153 (2017), pp 1779-1819. (arXiv:1311.0010)
9. Decorated marked surfaces (Part B): Topological realizations,
Math. Z. 288 (2018) pp 39–53.
10. Contractible stability spaces and faithful braid group actions, with J. Woolf,
Geom. & Topol. 22 (2018) 3701–3760. (arXiv:1407.5986)
11. DMS~II: Intersection numbers and dimensions of Homs, with Y.Zhou,
Trans. Amer. Math. Soc., 372(2019) 635–660. (arXiv:1411.40033)
12. The braid group for a quiver with superpotential,
Sci. China. Math. 62 (2019) 1241-1256. (arXiv:1712.09585)
13. DMS~III: The derived category of a decorated marked surface, with A. Buan and Y. Zhou,
Int. Math. Res. Notice. https://doi.org/10.1093/imrn/rnz180. (arXiv:1804.00094)
14. Cluster exchange groupoids and framed quadratic differentials, with A. King,
Invent. Math. 220 (2020) 479–523. (arXiv:1805.00030)
15. Topological structure of spaces of stability conditions and top. Fukaya type categories
Proceeding of First Annual Meeting of ICCM. .(arXiv:1806.00010)
16. Decorated Marked Surfaces: Calabi-Yau categories and related topics
Proceeding of the 51st Symposium on Ring Theory and Rep. Theory, Okayama, Japan (arXiv:1812.00008)
17. Finite presentations for spherical/braid twist groups from decorated marked surfaces, with Y. Zhou,
J. Topology. 13 (2020) 501-538. (arXiv:1703.10053)
18. Stability conditions and A2 quivers, with T. Bridgeland and T. Sutherland,
Adv. Math. 365 (2020) 107049. (arXiv:1406.2566)
Preprint
19. Frobenius morphisms and stability conditions, with W. Chang,
20. Global dimension function, Gepner equations and q-stability conditions.
21. q-Stability conditions on Calabi-Yau-X categories and twisted periods. with A. Ikeda,
22. q-Stability conditions via q-quadratic differentials for Calabi-Yau-X categories. with A. Ikeda,
23. Contractibility of space of stability conditions on the projective plane via global dimension function. with Yu-Wei Fan, Chunyi Li, and Wanmin Liu,
24. Graded decorated marked surfaces: Calabi-Yau-X categories of gentle algebras, with Akishi Ikeda and Yu Zhou,
25. Contractible flow of stability conditions via global dimension function.
姓名 | 职称 | 研究方向 | |
邱宇 | 教授 | 代数表示论/几何拓扑 | |
扶磊 | 教授 | 代数几何 | |
Caucher Birkar | 教授 | 双有理几何 | |
单芃 | 教授 | 几何表示论 | |
朱艺航 | 教授 | 代数数论、朗兰兹纲领 | |
盛茂 | 教授 | 代数几何 | |
刁晗生 | 副教授 | p 进几何以及其在 p 进霍奇理论中的应用;p 进模形式 | |
徐斌 | 副教授 | 自守形式,p-adic 群表示论 | |
Will Donovan | 副教授 | 代数几何 | |
Emmanuel Lecouturier | 副教授 | 数论 | |
曹晋 | 助理教授 | 代数几何 | |
何翔 | 助理教授 | 代数几何 | |
胡悦科 | 助理教授 | 理论数学 | |
李鹏辉 | 助理教授 | 顶点算子代数、数学物理 | |
李永雄 | 助理教授 | 数论 | |
张鼎新 | 助理教授 | D-模,刚性上同调,指数和,形式群 | |
郑志伟 | 助理教授 | 代数几何 | |
范祐维 | 助理教授 | 代数几何 | |
苏长剑 | 助理教授 | 表示论 | |
周宇 | 助理教授 | 代数表示论 |