Research Statement

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Synopsis

I am interested in mathematical modeling and analysis of problems in the physical sciences. Of particular concern to me is the combination of analysis and computational methods to gain insight into the mathematical structure and physical consequences of the model and its results. Further, I seek to work together with probabilists and to combine methods from analysis and probability theory to learn about the behavior of complex physical systems with random input. The major areas of my research are the fields of calculus of variations with nonconvex energy functionals and free boundary evolution problems.

Most of my research to date has been motivated by problems in plasticity or in phase transitions. Specifically, I have worked on the evolution of phase boundaries in heterogeneous media, the dislocation pattern formation in single crystal plasticity, and on the modeling and simulation of problems involving multi-well energies and higher gradient terms. I would like to build on this experience by working on interesting and relevant projects in the future.