I work on modular tensor categories. Most recently, my advisor Zhenghan Wang and I have been studying kernels of representations of the three-strand braid group arising from these categories. Our focus is on those representations arising from objects satisfying the Property F conjecture.
When I was at SUNY Buffalo, I worked on decomposing certain induced modules of the symmetric group (summarized in my undergraduate thesis below).
- (with Zhenghan Wang) Congruence subgroups from representations of the three-strand braid group. Journal of Algebra 487 (2017).(arXiv)
- Decomposing induced characters of the centralizer of an \(n\)-cycle in the symmetric group on \(2n\) elements, Involve