Research

During my graduate studies, I worked on a kind of elliptic system modelling the segregation phenomenon of multiple populations. The system is interesting, as it connects elliptic PDE, free boundary problems, geometric measure theory, mathematical modeling, etc. Together with Professor Monica Torres and Professor Stefania Patrizi, we proved lots of properties of the solutions of the elliptic system, and we also performed a detailed study of the regularity of the free boundary in the two-dimensional case. We also extended some of the known results in the two-dimensional case to higher dimensions. 

I am also interested in other fields and problems, including but not limited to: Calculus of Variations, Probability Theory, Dynamical Systems, Nonlocal Operators, Applied Math, etc.

 Please refer to "Publications" and "Research Statement" for more details.