I'm currently planning on working with the Applied group here at UCSB. I've been reading in the area of Optimal Transport with Dr Craig, with a focus on studying gradient flows in the Wasserstein spaces as a method for solving PDEs based on the continuity equation. This is called the Minimizing Movement scheme or the JKO Algorithm, and is an exciting numerical technique whose iterations are based on optimization problems, which gives finer controls on convergence rates than other schemes and allows for generalization to metric settings where more classical ideas of gradient flow break down. One of the most useful references for this is "Euclidean, Metric, and Wasserstein Gradient Flows" by Filippo Santambrogio (whose "Optimal Transport for Applied Mathematicians" is also excellent).

I completed an undergraduate thesis, Complexity of Linear Summary Statistics, exploring the asymptotic computational costs of computing families of linear functionals useful as summary statistics.