Yilong Wang

Personal Information

Name

Yilong Wang

Position

Associate Professor

Contact Information

Beijing Institute of Mathematical Sciences and Applications (BIMSA)
Huairou, Beijing, China.

Email Address:

wyl AT bimsa DOT cn

Research

Research Interests

Tensor category, topological field theory, low-dimensional topology.
Thesis advisor: Thomas Kerler.
Postdoc mentor: Siu-Hung Ng.

BIMSA-Tsinghua Quantum Symmetry Seminar

Curriculum Vitae

Last updated on Jun 14, 2022.

Publications and Preprints (Papers at arXiv.org)

1. Non-semisimple open-closed 3d TFT (with Ingo Runkel).
     arXiv: arXiv:2608.08057


2. Modular fusion categories with trivial Torelli group actions (with Liang Chang and Siu-Hung Ng).
     arXiv: 2608.04462


3. On the gauge invariance of the Kuperberg invariant of certain high genus framed 3-manifolds (with Liang Chang and Saifei Zhai).
     arXiv: 2601.19485


4. Generalized Witt and Morita equivalences (with Liang Kong and Hao Zheng).
     arXiv: 2511.02624


5. Generalizations of Frobenius-Schur indicators from Kuperberg invariants (with Liang Chang and Siu-Hung Ng).
     arXiv: 2506.07409


6. Alterfold Theory and Topological Modular Invariance (with Zhengwei Liu, Shuang Ming and Jinsong Wu).
     Comm. Math. Phys. 407(5), no. 102, 2026.
     doi:10.1007/s00220-026-05590-9
     arXiv: 2412.12702


7. Alterfold Topological Quantum Field Theory (with Zhengwei Liu, Shuang Ming and Jinsong Wu).
     Science China Math. 2026.
     doi:10.1007/s11425-025-2574-6
     arXiv: 2312.06477


8. 3-Alterfolds and quantum invariants (with Zhengwei Liu, Shuang Ming and Jinsong Wu).
     arXiv: 2307.12284


9. On symmetric representations of $\mathrm{SL}_2(\mathbb{Z})$ (with Siu-Hung Ng and Samuel Wilson).
     Proc. Amer. Math. Soc. 151 (2023), no. 4, 1415-1431.
     doi:10.1090/proc/16205
     arXiv: 2203.15701


10. The Witt classes of $\mathfrak{so}(2r)_{2r}$ (with Eric C. Rowell and Yuze Ruan).
      Comm. Algebra. 50 (2022), no. 12, 5246-5265.
      doi:10.1080/00927872.2022.2083630
      arXiv: 2107.06746


11. Modular categories with transitive Galois actions (with Siu-Hung Ng and Qing Zhang).
      Comm. Math. Phys. 390 (2022), no. 3, 1271-1310.
      doi:10.1007/s00220-021-04287-5"
      arXiv: 2007.01366


12. Higher central charges and Witt groups (with Siu-Hung Ng, Eric C. Rowell and Qing Zhang).
      Adv. Math. 404 (2022), Paper No. 108388.
      doi:10.1016/j.aim.2022.108388
      arXiv: 2002.03570


13. Classification of spherical fusion categories of Frobenius-Schur exponent 2 (with Zheyan Wan).
      Algebra Colloq. 28 (2021), no. 1, 39-50.
      doi:10.1142/S1005386721000055
      arXiv: 1811.02004


14. Higher Gauss sums of modular categories (with Siu-Hung Ng and Andrew Schopieray).
      Selecta Math. (N. S.) 25 (2019), no. 4, Art 53, 32pp.
      doi:10.1007/s00029-019-0499-2
      arXiv: 1812.11234


15. On modular group representations associated to SO$(p)_2$-TQFTs.
      J. Knot Theory Ramifications 28 (2019), no. 5, 1950037, 20 pp.
      doi:10.1142/S0218216519500378
      arXiv: 1702.03798


16. Random walk invariants of string links from R-matrices (with Thomas Kerler).
      Algebr. Geom. Topol. 16 (2016), no. 1, 569--596.
      doi:10.2140/agt.2016.16.569
      arXiv: 1406.2722


17. On integrality of SO(n)-Level-2 TQFTs. Thesis

Notes

1. On the positivity conjecture


2. Prime factorizations in modular categories

Teaching