1. Partial Differential Equations
Most interested in various estmate methods including gradient estimate. Work on second order elliptic and hyperbolic equations, especially of Laplacian and its eigenvalue problems.

2. Analysis and Topology
Interested in Harmonic Analysis and Functional Analysis. Especially the applications in PDE. For Topology field, I am interested in Knot Theory.

3. Inverse Problem
Followed my supervisor Shumin Li during 2010-2011, studying the hyperbolic cases inverse problems. Now I am following my mentor Kui Ren on inverse problem.