My main interest in mathematics is on higher representation theory, algebraic geometry, and their applications to low-dimensional topology. Currently, I'm working on categorification of small quantum groups-a special kind of finite dimensional Hopf algebra, and trying to construct a four-dimensional topological quantum field theory out of them. This is the original motivation of categorification initiated by Louis Crane and Igor Frenkel. The picture on the top-right is a categorical interpretation of one of the so called quantum Serre relations for the small quantum group sl(3). I'm also looking into the algebro-geometric meaning behind the small quantum groups.

More information about my past experience is contained in my CV. Further details on my earlier work, ongoing projects, and future plans can be found in my research statement.

Research partially funded by the National Science Foundation, DMS-1763328.