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Research Interests

I study discrete dynamical systems, specifically integrable systems. In my dissertation we used a family of integrable systems to solve several problems related to orthogonal polynomials and enumerating regular maps on Riemann surfaces. The pdf below is a short, conversational summary of the problems addressed in my thesis. Dissertation Summary

Here is an extended abstract on dynamical systems in the complex setting: Complex Dynamics

I have also worked on isoperimetric problems and Sobolev inequalities for negative curvature spaces.