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)


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