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研究方向概况

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,

arXiv:1210.0243

20. Global dimension function, Gepner equations and q-stability conditions.

arXiv:1807.00010

21. q-Stability conditions on Calabi-Yau-X categories and twisted periods. with A. Ikeda,

arXiv:1807.00469

22. q-Stability conditions via q-quadratic differentials for Calabi-Yau-X categories. with A. Ikeda,

arXiv:1812.00010

23. Contractibility of space of stability conditions on the projective plane via global dimension function. with Yu-Wei Fan, Chunyi Li, and Wanmin Liu,

arXiv:2001.11984

24. Graded decorated marked surfaces: Calabi-Yau-X categories of gentle algebras, with Akishi Ikeda and Yu Zhou,

arXiv:2006.00009

25. Contractible flow of stability conditions via global dimension function.

arXiv:2008.00282



科研团队

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