My research focuses on mathematical structures arising from both classical and quantum statistical physics. These structures emerge out of fundamental questions in physics, primarily asking how to approximate high or infinite dimensional many-body dynamics by effective non-linear PDEs.
I plan to continue studying these types of problems in mathematical physics, and additionally investigate how to apply these methods to problems in large neural networks. This approach to studying machine learning has the potential to utilize the high dimensionality of these networks and understand how they converge at the level of rigor of mathematical physics.