Research Area: Analysis, Applied Mathematics

Research Profile: Nonlinear partial differential equations, mathematical physics.
I work in the areas of elliptic partial differential equations, the calculus of variations, and mathematical physics. Elliptic PDEs often arise as stationary equilibria in physical problems or in describing curved surfaces in differential geometry. The calculus of variations is concerned with extrema (critical points) of functions defined on infinite dimensional spaces. For example, solutions to the Dirichlet problem minimize an associated integral among all functions with the given boundary data ("Dirichlet's Principle"). This observation, known to Gauss and Riemann, introduced variational methods as a tool in studying elliptic PDEs. Today we use a combination of classical variational techniques, real and functional analysis, and topology to study existence, multiplicity, smoothness, stability, and other qualitative properties of solutions to PDEs. Of particular interest are those problems (arising in physics and geometry) where minimizing sequences may not converge, due to the natural symmetries of the problem.

Nonlinear partial differential equations, mathematical physics

2021/2022
Math 3A03
Math 4A03/6A03
Math 721

2020/2021
Math 3A03
Math 3IA3
Math 4A03/6A03

2019/2020
Math 3A03

2018/2019
Math 2XX3
Math 3A03
Math 3DC3

2017/2018
Math 2XX3
Math 748

2016/2017
Math 1X03
Math 2XX3
Math 721

2015/2016
Math 1X03
Math 2XX3
Math 721

2014/2015
Math 1XX3
Math 4A03/6A03
Math 742

2013/2014
Math 2C03
Math 4A03/6A03
Math 721