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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.

• 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. For applications, cf. [4,6,10].
• 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).
• 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.
• q-Deformation of stability conditions
  In [18,21], 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].
  
• Global dimension (glidm) function
  As a byproduct of [18,21], 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].
• Quadartic differentials as stability condtiions (FQuad=Stab)
  Following Bridgeland-Smith, we prove various such correspondences with various applications, cf. [15,21,23,28,34,35].
• Twist groups and cluster braid groups
  We introduce the braid twist group in [7] (cf. [14,35]) and cluster braid groups in [15] (cf. [25]) as generalizations of Artin braid groups. In various cases, they can be identifed with spherical twist groups (of Calabi-Yau categories).
• Categorical/Geometric K(π,1)-conjecture for braid/twist groups
  By FQuad=Stab, we aim to prove the contractibility of various moduli spaces, may be regarded as different version of K(π,1)-conjecture. For developments, cf. [10,7,15,35].

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-)
卢穗麒 Lu Suiqi (2022-)

Postdocs:

王起 Wang Qi (2022-2025)
何平 He Ping (2022-2025)
大谷拓己 Otani Kamumi (2023-2026)

Publications

Preprints

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 Verdier quotients of Calabi-Yau categories from quivers with potential, with Anna Barbieri,
arxiv:2411.00207

38 Perverse schobers, stability conditions and quadratic differentials II: relative graded Brauer graph algebras, with Merlin Christ and Fabian Haiden,
arxiv:2407.00154

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

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

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

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

33 Perverse schobers, stability conditions and quadratic differentials I, with Merlin Christ and Fabian Haiden,
arxiv:2303.18249

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

31 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 17 (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. q-Stability conditions via q-quadratic differentials, with Akishi Ikeda,
    Memoirs of Amer. Math. Soc. to appear. arXiv:1812.00010
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. Cluster braid groups of Coxeter-Dynkin diagrams, with Zhe Han and Ping He,
    J. Comb. Theory (A), 208 (2024), 105935. (arXiv:2310.02871)
26. Topological model for q-deformed rational number and categorification, with Li Fan,
    Rev. Mat. Iberoam., to appear. (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 triangulation categories, with Xiaoting Zhang,
    Selecta Math. to appear. (aXiv:2310.02917)

Proceedings

1. 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)
2. 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