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邱宇 Qiu Yu

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Personal informaiton

Position: Professor @
Yau Mathematical Sciences Center, Tsinghua University
Email: yu.qiu@bath.edu
Address: Shuangqing Complex Building C650
Tsinghua University
Beijing 100084, China

Research interest:

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 quivers (with potentials), Calabi-Yau/Fukaya categories, stability conditions, braid groups, cluster theory and moduli spaces.

• Non-asphericity of strata of genus-one differentials and stability spaces
  We show that when the number of zeros or poles is at least four, every connected component of the strata of differentials in genus one with prescribed zero and pole orders is not an orbifold K(π,1). For quadratic differentials, this provides infinitely many counterexamples to a conjecture attributed to Kontsevich, as well as to a folklore conjecture concerning the contractibility of spaces of Bridgeland stability conditions, cf. [43].
• X-evolution flow on cluster complexes
  We introduce flows and foliations on cluster complexes, motivated by Hatcher’s flow on arc complexes (but different). It turns out to be a countinous refinement/generalization of green mutation (on cluster exchange graphs) with application to understand the topology of cluster complexes, cf. [40].
• Twist groups and cluster braid groups
  We introduce the braid twist group in [7] (cf. [14,42]) and cluster braid groups in [15] (cf. [21]) as generalizations of Artin braid groups. In various cases, they can be identifed with spherical twist groups (of Calabi-Yau categories).
• Quadartic differentials as stability condtiions (FQuad=Stab)
  Following Bridgeland-Smith, we prove various such correspondences with various applications, cf. [15,23,25,28,30].
• Global dimension (glidm) function
  As a byproduct of [18,25], we introduce gldim function (kind of piece-wise Morse) on Stab in [17] and define the gldim for a triangulated category. See further development [19,24].
• q-Deformation of stability conditions
  In [18,25], we introduce a q-deformation of triangulated categories and the stability conditions on which. Motivation comes from the study of (almost) Frobenius structure on the spaces Stab of stability conditions, cf. [13].
  
• Geometric model for skew-gentle type categories
  Similar to DMS series, we introduce geometric models for various categories, cf. [8,5,32,36], with various realization of Z_2-symmetry.
• Decorated Marked Surfaces (DMS)
  In DMS series [7,9,11,16,14,15], we introduce DMS as a topological/geometric model for 3-Calabi-Yau categories associated to quivers with potential from triangulated marked surfaces (without punctures).
• Simple tilting theory
  In [3], we introduce the exchange graphs of (finite) hearts, which can be identified with exchange graphs of silting objets via simple-projective duality. They are skeleton of spaces of stability conditions. Moreover, we show that exchange graphs of hearts in N-Calabi-Yau categories are spherical-twist covering of the (N-1)-cluster exchange graphs. For applications, cf. [4,6,10].

Students:

李子戌 Li Zixu (2019-2024, co-sup. by Zhou Yu)
吴东箭 Wu Dongjian (2020-2025)
范俐 Fan Li (2021- , co-sup. by Bernhard Keller)
卢穗麒 Lu Suiqi (2022-)
汤立恒 Tang Liheng (2025-)
陈思遇 Chen Siyu (2026-)

Postdocs:

王起 Wang Qi (2022-2025)
何平 He Ping (2022-2025)
大谷拓己 Otani Kamumi (2023-2026)
孟成 Meng Cheng (2024-2027)
刘绵涛 Liu miantao (2026-2029)

Publications

Preprints

43 Non-asphericity of strata of genus-one differentials and stability spaces, with Dawei Chen, Jingyin Huang and Fei Yu,
arxiv:2606.24135

42 Decorated Marked Surfaces with vortices: Cluster braid group vs. braid twist group, with Yu Zhou,
arxiv:2511.00438

41 Contractibility and total semi-stability conditions of Euclidean quivers, with Xiaoting Zhang,
arxiv:2501.16903

40 From mutation to X-evolution: flows and foliations on cluster complexes, with Liheng Tang,
arxiv:2501.15756

39 Dg enhanced orbit categories and applications, with Li Fan and Bernhard Keller,
arxiv:2405.00093

38 A geometric realization of Koszul duality for graded gentle algebras, with Zixu Li and Yu Zhou,
aXiv:2403.15190

37 Moduli spaces of quadratic differentials: Abel-Jacobi map and deformation,
aXiv:2403.10265

36 Quadratic Differentials as Stability Conditions of Graded Skew-gentle Algebras, with Suiqi Lu and Dongjian Wu,
aXiv:2310.20709

35 Two geometric models for graded skew-gentle algebras, with Chao Zhang and Yu Zhou,
arxiv:2212.10369

34 Graded decorated marked surfaces: Calabi-Yau-X categories of gentle algebras, with Akishi Ikeda and Yu Zhou,
arXiv:2006.00009

Papers

1. On the focus order of planar polynomial differential equations, with Jiazhong Yang,
   J. Diff. Equations, 246 (2009), 3361-3379.
2. Ext-quivers of hearts of A-type and the orientation of associahedron,
   J. Algebra, 393 (2013), 60-70. (arXiv:1202.6325)
3. Exchange graphs and Ext quivers, with Alastair King,
   Adv. Math. 285 (2015), 1106–1154. (arXiv:1109.2924)
4. Stability conditions and quantum dilogarithm identities for Dynkin quivers,
   Adv. Math. 269 (2015), 220-264. (arXiv:1111.1010)
5. Tagged mapping class group: Auslander-Reiten translations, with Thomas Brüstle,
   Math. Zeit. 279 (2015), 1103-1120. (arXiv:1212.0007)
6. C-sortable words as green mutation sequences,
   Proc. Lond. Math. Soc. 111 (2015), 1052-1070. (arXiv:1205.0034)
7. Decorated marked surfaces: Spherical twists versus braid twists,
   Math. Ann. 365 (2016), 595-633. (arXiv:1407.0806).
8. Cluster categories for marked surfaces: punctured case, with Yu Zhou,
   Compos. Math. 153 (2017), 1779-1819. (arXiv:1311.0010)
9. Decorated marked surfaces (Part B): Topological realizations,
   Math. Zeit. 288 (2018) 39–53.
10. Contractible stability spaces and faithful braid group actions, with Jon Woolf,
    Geom. & Topol. 22 (2018) 3701–3760. (arXiv:1407.5986)
11. DMS~II: Intersection numbers and dimensions of Homs, with Yu Zhou,
    Trans. Amer. Math. Soc. 372(2019) 635–660. (arXiv:1411.4003)
12. The braid group for a quiver with superpotential,
    Sci. China. Math. 62 (2019) 1241–1256. (arXiv:1712.09585)
13. Stability conditions and A2 quivers, with Tom Bridgeland and Tom Sutherland,
    Adv. Math. 365 (2020), 107049. (arXiv:1406.2566)
14. Finite presentations for spherical/braid twist groups, with Yu Zhou,
    J. Topology . 13 (2020) 501-538. (arXiv:1703.10053)
15. Cluster exchange groupoids and framed quadratic differentials, with Alastair King,
    Invent. Math. 220 (2020) 479–523. (arXiv:1805.00030)
16. DMS~III: The derived category of a decorated marked surface, with Aslak Buan and Yu Zhou,
    Int. Math. Res. Notices 2021 (2021) 12967-12992. (arXiv:1804.00094)
17. Global dimension function on stability conditions and Gepner equations,
    Math. Zeit. 303 (2023) No.11. (arXiv:1807.00010)
18. q-Stability conditions on Calabi-Yau-X categories, with Akishi IKeda,
    Compos. Math. 159 (2023), 1347–1386. (arXiv:1807.00469)
19. Contractibility of space of stability conditions on the projective plane via global dimension function with Yu-Wei Fan, Chunyi Li, and Wanmin Liu,
    Math. Res. Letter 30 (2023), 51–87. (arXiv:2001.11984)
20. Frobenius morphisms and stability conditions, with Wen Chang,
    Publ. Res. Inst. Math. Sci. 60 (2024), 271–303. (arXiv:1210.0243)
21. Cluster braid groups of Coxeter-Dynkin diagrams, with Zhe Han and Ping He,
    J. Comb. Theory (A), 208 (2024), 105935. (arXiv:2310.02871)
22. Geometric model for module categories of Dynkin quivers via hearts of total stability conditions, with Wen Chang and Xiaoting Zhang,
    J. Algebra 638 (2024), 57-89. (arxiv:2208.00073)
23. Quadratic differentials as stability conditions: collapsing subsurfaces, with Anna Barbieri, Martin Möller and Jeonghoon So,
    J. reine angew. Math. (Crelle’s Journal) 810 (2024), 49-95. (arxiv:2212.08433)
24. Contractible flow of stability conditions via global dimension function.
    J. Diff. Geom. 129 (2025), 491-521. (arXiv:2008.00282)
25. q-Stability conditions via q-quadratic differentials, with Akishi Ikeda,
    Memoirs of Amer. Math. Soc. 308 (2025), No. 1557. (arXiv:1812.00010)
26. Topological model for q-deformed rational number and categorification, with Li Fan,
    Rev. Mat. Iberoam., 41 (2025), 1337–1366. (arxiv:2306.00063)
27. Geometric classification of totally stable stability spaces, with Xiaoting Zhang,
    Math. Zeit. 309 (2025) No.58. (arxiv:2202.00092)
28. Fusion-stable structures on triangulated categories, with Xiaoting Zhang,
    Selecta Math. 31 (2025) No.50. (aXiv:2310.02917)
29. Perverse schobers, stability conditions and quadratic differentials II: relative graded Brauer graph algebras, with Merlin Christ and Fabian Haiden,
    Selecta Math., 32 (2026) No.62. (arxiv:2407.00154)
30. Verdier quotients of Calabi-Yau categories from quivers with potential, with Anna Barbieri,
    Doc. Math., to appear. (arxiv:2411.00207)
31. Perverse schobers, stability conditions and quadratic differentials I, with Merlin Christ and Fabian Haiden,
    Compos. Math., to appear. (arxiv:2303.18249)

Proceedings

32 Topological structure of spaces of stability conditions and top. Fukaya type categories,
Proceedings of the International Consortium of Chinese Mathematicians (2017) 521–538, Int. Press, Boston, MA, 2020. (arXiv:1806.00010)

33 Decorated Marked Surfaces: Calabi-Yau categories and related topics,
Proceeding of the 51st Symposium on Ring Theory and Rep. Theory, 129–134, Symp. Ring Theory Represent. Theory Organ. Comm., Shizuoka, 2019. (arXiv:1812.00008)

Editoral Board

Journal of the Korean Mathematical Society

Useful Links

• Other links:
  • YMSC
  • arXiv.RT // GT // AG
  • MathSciNet