My current work with Dr. Shankar Venkataramani is concerned with deriving rigorous bounds for a recursion process that comes from studying surfaces with constant negative Gaussian curvature equal to -1. For more information on the recursion process please see the paper  Distributed Branch Points and the Shape of Elastic Surfaces with Constant Negative Curvature by Toby L. Shearman & Shankar C. Venkataramani. Our hope is that this analysis will allow us to rigorously state that surfaces which allow for a certain topological defect, branch points, have a better energy scaling than those that do not allow for branch points.

I spent the summer of 2023 working at LANL with Dr. Alexander Scheinker, the team leader for adaptive machine learning in the applied electrodynamics group, and Dr. Christopher Leon, a postdoctoral research associate in the same group. I started the summer with investigating 2D MHD simulations that used the finite volume method and constrained transport. We then used an encoder-decoder neural network to predict features of the MHD simulations and to replace parts of the simulation. Our work culminated in the paper Solving the Orszag–Tang vortex magnetohydrodynamics problem with physics-constrained convolutional neural networks. This paper was featured on the front page of the journal Physics of Plasmas.