Research Interests:

Richard Ng is a member of the Algebra and Number Theory group of LSU. His current research interests lie in the area of Hopf algebras, quasi-Hopf algebras, spherical fusion categories, modular tensor categories and their applications in the representations of vertex operator algebras, quantum computations and condense matter physics. He and his collaborator have developed the arithmetic invariants of spherical fusion categgories, called the generalized Frobenius-Schur indicators, which allow these applications possible. This endeavor involves close ties with many other areas of mathematics such as number theory, representations of finite dimensional algebras and groups, quantum groups, invariants of 3-manifolds and the broadly conceived area of physical mathematics called conformal field theory.

Selected Publications : publications after 1997, MathSciNet, ArXiv.org and Google Scholar

  1. Higher central charges and Witt groups (with E. Rowell, Y. Wang, Q. Zhang), Advances in Mathematics 404 (2022) 108388 arXiv:2002.03570.

  2. Higher Gauss sums of modular categories (with A. Schopieray, Y. Wang), Selecta Math. (N.S.) 25 (2019), no. 4, Paper No. 53, 32 pp arXiv:1812.11234 .

  3. Rank-Finiteness for Modular Categories (with P. Bruillard, E. Rowell and Z.Wang), Journal of the American Mathematical Society, 29 (2016), no.3, 857--881, DOI: 10.1090/jams/842 (arXiv:1310.7050).

  4. Congruence property in Conformal Field Theory (with C. Dong and X. Lin), Algebra & Number Theory, 9 (2015), no. 9, 2121--2166, arXiv:1201.6644.

  5. Cleft Extensions and Quotients of Twisted Quantum Doubles (with G. Mason), Developments and retrospectives in Lie theory, 229--246, Dev. Math., 38, Springer, Cham, 2014, arXiv:1404.2016.

  6. On the trace of the antipode and higher indicators (with Y. Kashina and S. Montgomery), Israel Journal of Mathematics, 188 (2012), no.1, 57--89.

  7. Congruence Subgroups and Generalized Frobenius-Schur Indicators (with P. Schauenburg), Communications in Mathematical Physics, 300 (2010), no. 1, 1--46.

  8. Hopf algebras of dimension 2p2 (with M. Hilgemann), Journal of London Mathematical Society, 80 (2009) no. 2, 295-310.

  9. Frobenius-Schur Indicators and Exponents of Spherical Categories (with P. Schauenburg), Advances in Mathematics, 211 (2007), no. 1, 34--71.

Selected Organized Conferences/Workshops :

  1. AMS special session on Hopf Algebras and Tensor Categories, in Joint Mathematics Meeting, April 7-8, 2022 (with Tucker and Plavnik).

  2. Modular Categories--Their Representations, Classification, and Applications, Banff International Research Station, Oaxaca, Mexico, August 14-19, 2016 (with Nikshych, Rowell, and Wang).

  3. AMS MRC: Mathematics of Quantum Phases of Matter and Quantum Information, Snowbird Resort, Utah, June 24-30, 2014 (with Rowell, and Wang).

  4. AIM Workshop:SQuaRE on Classifying modular categories, August 10-15, 2015 (with Bruillard, Galindo, Plavnik, Rowell, and Wang).

  5. AMS special session on Hopf Algebras and Tensor Categories in Joint Mathematics Meeting, San Antonio, January 10-13, 2015 (with Montgomery and Witherspoon).

  6. AIM Workshop:SQuaRE on Classifying modular categories, May 19-23, 2014 (with Bruillard, Galindo, Plavnik, Rowell, and Wang).

  7. AMS special session on Hopf Algebras, Coalgebras, and their Categories of Representations in the Joint International AMS-RMS Meeting, Alba Iulia, Romania, June 27-30, 2013 (with Montgomery and Iovanov).

  8. Workshop on Fusion Categories, Institut de Mathématiques de Bourgogne, Université de Bourgogne, May 21-23, 2013 (with Schauenburg).