About Me

I am a differential geometer working on surface theory and its applications to biology, physics, and data science. I received my PhD from Texas Tech University under the guidance of Prof. Magdalena Toda, with co-advisors Prof. Hung Tran and Prof. Eugenio Aulisa.

My research interests include surface immersions, curvature functionals, variational calculus, computational and discrete geometry, integrability problems, conformal geometry, and geometric flows.

Below are some snapshots of my recent work. See my research page for further details.

  • Modeling the p-Willmore flow of surfaces

    Geometric flows are beautiful and powerful tools for prescribing a change in the geometry of a surface. This project is a computational study of the p-Willmore flow, with the aim to develop a finite-element model that is amenable to geometric constraints on surface area and enclosed volume. (Joint with Eugenio Aulisa.)

  • Active Manifolds: geometric data analysis for dimension reduction

    Scientists and engineers are frequently presented with mathematical models that are difficult to analyze due to their reliance on a large number of parameters. This project is inspired by the Active Subspaces idea of Paul Constantine, and provides an algorithm which reduces the dimension of an unknown function to 1 regardless of the size of the original input space. (Joint with Robert Bridges.)