- Geometric Partial Differential Equations (PDEs)
- Numerical analysis and Finite Element Methods (FEM)
- Liquid crystals
- Geometric evolution and surface FEM
- Optimal control of PDEs
I work in the area of Geometric Partial Differential Equations (PDEs) involving mathematical modeling, numerical analysis, and finite element methods (FEM). The hallmark of Geometric PDEs is a crucial structural component involving geometry that is central to the phenomena that the PDEs model. Examples are liquid crystals, PDEs on surfaces/manifolds, free boundary and geometric evolution problems (e.g. surface tension driven motion), and optimal control of PDEs.
Check out the cool math music video I made on this page.