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


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


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


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


5. 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


6. 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


7. 3-Alterfolds and quantum invariants (with Zhengwei Liu, Shuang Ming and Jinsong Wu).
     arXiv: 2307.12284


8. 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


9. 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


10. 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


11. 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


12. 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


13. 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


14. 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


15. 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


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

Notes

1. On the positivity conjecture


2. Prime factorizations in modular categories

Teaching