short line

Research Interests

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).