Research Interests:

Richard Ng's present research interests lie in the area of Hopf algebra, quasi-Hopf algebra and tensor category. The main focus at the moment is aimed at the classification of finite dimensional Hopf algebras in special dimensions, and the study of invariants of pivotal tensor categories such as Frobenius-Schur indicators and exponents. This endeavor involves close ties with many other areas of mathematics such as representations of finite dimensional algebras and groups, knot invariants, etc. and the broadly conceived area of physical mathematics called conformal field theory.

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

  1. 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).
  2. Congruence property in Conformal Field Theory (with C. Dong and X. Lin), Algebra & Number Theory, 9 (2015), no. 9, 2121--2166, arXiv:1201.6644.
  3. 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.
  4. 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.
  5. Congruence Subgroups and Generalized Frobenius-Schur Indicators (with P. Schauenburg), Communications in Mathematical Physics, 300 (2010), no. 1, 1--46.
  6. Hopf algebras of dimension 2p2 (with M. Hilgemann), Journal of London Mathematical Society, 80 (2009) no. 2, 295-310.
  7. Frobenius-Schur Indicators and Exponents of Spherical Categories (with P. Schauenburg), Advances in Mathematics, 211 (2007), no. 1, 34--71.

Organized Conferences/Workshops :

  1. Modular Categories--Their Representations, Classification, and Applications, Banff International Research Station, Oaxaca, Mexico, August 14-19, 2016 (with Nikshych, Rowell, and Wang).
  2. AMS MRC: Mathematics of Quantum Phases of Matter and Quantum Information, Snowbird Resort, Utah, June 24-30, 2014 (with Rowell, and Wang).
  3. AIM Workshop:SQuaRE on Classifying modular categories, August 10-15, 2015 (with Bruillard, Galindo, Plavnik, Rowell, and Wang).
  4. AMS special session on Hopf Algebras and Tensor Categories in Joint Mathematics Meeting, San Antonio, January 10-13, 2015 (with Montgomery and Witherspoon).
  5. AIM Workshop:SQuaRE on Classifying modular categories, May 19-23, 2014 (with Bruillard, Galindo, Plavnik, Rowell, and Wang).
  6. 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).
  7. Workshop on Fusion Categories, Institut de Mathématiques de Bourgogne, Université de Bourgogne, May 21-23, 2013 (with Schauenburg).