Published

1. Ore's theorem for cyclic subfactor planar algebras and beyond, Pacific J. Math. 292-1 (2018), 203-221, DOI: 10.2140/pjm.2018.292.203, arXiv:1702.02124,

2. On Boolean intervals of finite groups (with Mamta Balodi), J. Combin. Theory Ser. A 157 (2018), 49-69, DOI:10.1016/j.jcta.2018.02.004, arXiv:1604.06765,

3. Dual Ore's theorem on distributive intervals of finite groups, J. Algebra, 505 (2018), 279-287, DOI:10.1016/j.jalgebra.2018.03.017, arXiv:1708.02565,

4. Euler totient of subfactor planar algebras. Proc. Amer. Math. Soc. 146 (2018), no. 11, 4775–4786, DOI: 10.1090/proc/14167, arXiv:1703.04486.

5. Ore's theorem on subfactor planar algebras, Quantum Topology, 11 (2020), no. 3, 525–543, DOI: 10.4171/QT/141, arXiv:1704.00745.

6. Boolean lattices in finite alternating and symmetric groups (with Andrea Lucchini, Mariapia Moscatiello and Pablo Spiga), Forum Math. Sigma, 8 (2020), E55, DOI:10.1017/fms.2020.49, arXiv:1911.04516.

7. Fusion Bialgebras and Fourier Analysis (with Zhengwei Liu and Jinsong Wu), Adv. Math. 390 (2021), Paper No. 107905, 63 pp, DOI: 10.1016/j.aim.2021.107905, arXiv:1910.12059.

8. Classification of Grothendieck rings of complex fusion categories of multiplicity one up to rank six (with Zhengwei Liu, Yunxiang Ren), Lett. Math. Phys. 112 (2022), no. 3, Paper No. 54, 37 pp. DOI: 10.1007/s11005-022-01542-1, shared link, arXiv:2010.10264.

9. Interpolated family of non group-like simple integral fusion rings of Lie type (with Zhengwei Liu and Yunxiang Ren), Internat. J. Math. 34 (2023), no. 6, Paper No. 2350030, 51 pp., DOI: 10.1142/S0129167X23500301, arXiv:2102.01663.

10. Complete Positivity of Comultiplication and Primary Criteria for Unitary Categorification (with Linzhe Huang, Zhengwei Liu and Jinsong Wu), Int. Math. Res. Not. IMRN (2024), no.1, 817–860. DOI: 10.1093/imrn/rnad214, arXiv:2210.00792.

Accepted

Under review

• Triangular prism equations and categorification (with Zhengwei Liu and Yunxiang Ren), arXiv:2203.06522, 33 pages.

• Structure constants, Isaacs property and Extended-Haagerup fusion categories (with Sebastian Burciu), arXiv:2210.13936, 11 pages.

• Classification of integral modular data up to rank 13 (with Max A. Alekseyev, Winfried Bruns, Fedor V. Petrov), arXiv:2302.01613, 34 pages.

• Burnside type results for fusion categories (with Sebastian Burciu), arXiv:2302.07604, 61 pages.

Works in progress

• Classification of simple integral fusion rings (with Winfried Bruns),

• Polynomial Equations for Irrational Near Group Categories (with Zhengwei Liu and Yunxiang Ren),

• Watatani's theorem and Ore's theorem on tensor categories (with Keshab Chandra Bakshi and Mainak Ghosh).

Simple integral fusion rings (2019-2020)

The following documents should be seen as an extended appendix to the above paper Fusion Bialgebras and Fourier Analysis (with Zhengwei Liu and Jinsong Wu):

Go to the following sections of the new Atlas of Fusion Rings: 

• Simple integral fusion rings of Frobenius type,

• SageMath codes for classifications and criterions

Unpublished

• The Boolean intervals of Chevalley type are strongly non group-complemented (with Pablo Spiga), arXiv:1911.06076, 4 pages.

• Dual Ore's theorem for distributive intervals of small index, arXiv:1610.07253, 15 pages,

• Ore's theorem for cyclic subfactor planar algebras and application, arXiv:1505.06649, 50 pages,

• Neveu-Schwarz and operator algebras I: Vertex operator superalgebra, arXiv:1010.0078, 40 pages,

• Neveu-Schwarz and operator algebras II: Unitary series and characters, arXiv:1010.0077, 30 pages,

• Neveu-Schwarz and operator algebras III: Subfactors and Connes fusion, arXiv:1010.0076, 54 pages.

Errata

• arXiv:1505.06649, proof of Theorem 5.2:  there is a gap in the proof. The reader should consider Propositions 4.18 and 4.21 of the short version arXiv:1702.02124.

• arXiv:1702.02124, Conjectures 6.2 and 6.16:  'less than' should be 'at most' (it is corrected in the published version),

• published paper 3, Lemmas 3.7 and 3.8:  'finite dimensional' should be 'irreducible' (it is corrected on arXiv).

• published paper 4,  proof of Theorem 5.1, first claim: $[\alpha_i, \hat{1}]$ must be replaced by $[\emptyset, \alpha_i]$.

• published paper 9, in the statement of Theorem 5.2, the case sVec is missing (fortunately, no incidence on the rest of the paper).

Old drafts

• The type III manufactory, arXiv:1101.2827, 9 pages,

• Spectral triples for finitely presented groups, index 1, arXiv:1011.4436, 6 pages,

• Spectral triples for finitely generated groups, index 0, arXiv:1010.5221, 7 pages.

Extra material

• Old version (2013) of SageMath code for simple integral fusion rings (pdf, 2013) the first examples pdf and extra (see slides 21-31). New Atlas of Fusion Rings.

• PhD Dissertation, Unitary discrete series, characters, Connes fusion and subfactors for the Neveu-Schwarz algebra, (2009), HAL Id: tel-00514234, 155pp.

• Panorama around the Virasoro algebra (2009) pdf.