## Research Interests

- Partial Differential Equations (PDEs) related to fluids and moving boundaries
- Free boundary and geometric evolution problems
- Numerical analysis and finite element methods (FEM)
- Liquid crystals
- Mesh generation
- Optimal control of PDEs and shape optimization

I am currently

**recruiting PhD students.**See Student Projects for more information.

I work on various problems in continuum mechanics, such as fluid models and elasticity. Some of my work is on free boundary/moving interface problems where geometry plays a critical role (for example two-phase fluid flows driven by surface tension). Often these problems involve different physical models that are coupled together (such as fluids interacting with electric fields). A primary focus of my research is on mathematical modeling and numerical analysis of **liquid crystals**. I also work on shape optimization with PDE-constraints. The main aspects of my work are mathematical modeling, PDE theory, and FEM.

Check out the cool

**math music video**I made on this page.

This material is based upon work supported by the National Science Foundation under the following grants:

DMS-1115636,
DMS-1418994,
DMS-1555222 (**CAREER**).