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.
publications after 1997,
for Modular Categories (with P. Bruillard, E. Rowell and Z.Wang),
Journal of the American Mathematical Society,
29 (2016), no.3, 857--881,
property in Conformal Field Theory (with C. Dong and X. Lin), Algebra
& Number Theory, 9 (2015), no. 9, 2121--2166,
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.
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.
Subgroups and Generalized Frobenius-Schur Indicators (with P. Schauenburg),
Communications in Mathematical Physics, 300 (2010), no. 1, 1--46.
Hopf algebras of dimension 2p2 (with M. Hilgemann), Journal of London
Mathematical Society, 80 (2009) no. 2, 295-310.
and Exponents of Spherical Categories (with P. Schauenburg), Advances in
Mathematics, 211 (2007), no. 1, 34--71.
Organized Conferences/Workshops :
Categories--Their Representations, Classification, and Applications, Banff
International Research Station, Oaxaca, Mexico, August 14-19, 2016 (with
Nikshych, Rowell, and Wang).
- AMS MRC:
Mathematics of Quantum Phases of Matter and
Quantum Information, Snowbird Resort, Utah, June 24-30, 2014
(with Rowell, and Wang).
- AIM Workshop:SQuaRE on Classifying modular categories, August
10-15, 2015 (with Bruillard, Galindo, Plavnik, Rowell, and Wang).
- AMS special
session on Hopf
Algebras and Tensor Categories in Joint Mathematics Meeting, San Antonio,
January 10-13, 2015 (with Montgomery and Witherspoon).
- AIM Workshop:SQuaRE on Classifying modular categories, May
19-23, 2014 (with Bruillard, Galindo, Plavnik, Rowell, and Wang).
- AMS special
session on Hopf Algebras,
Coalgebras, and their Categories of Representations in
International AMS-RMS Meeting, Alba Iulia, Romania, June 27-30, 2013 (with
Montgomery and Iovanov).
- Workshop on
Fusion Categories, Institut de Mathématiques de Bourgogne, Université
de Bourgogne, May 21-23, 2013 (with Schauenburg).