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Research Interests

I am currently recruiting PhD students. See Student Projects for more information.

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.

This material is based upon work supported by the National Science Foundation under the following grants:
DMS-1115636, DMS-1418994, DMS-1555222 (CAREER) DMS-2111474.