I'm interested in fluid mechanics, parabolic partial differential equations, stochastic PDEs, machine learning, signal processing, optimal transport, approximation theory, wavelets, and numerical PDEs
Here are a list of my papers:
Non-Decaying Solutions to the 2D Dissipative Quasi-Geostrophic Equations (w/ James Kelliher, Elaine Cozzi, and David Ambrose) https://arxiv.org/abs/2508.10254
Existence Results for the Dissipative and Inviscid Surface Quasi‑Geostrophic Equations
Global-in-time $L^2_{ul} weak solutions to the 2D Quasi-Geostrophic equations (w/ James Kelliher, Elaine Cozzi, and David Ambrose) (in preparation)
Bridging Diffusion Models and PDEs: Solving Fokker–Planck Equations Using Minimum Sobolev Norm Approximation (w/ Hrushikesh Mhaskar) (in preparation).
On a priori estimates for nonlinear rough PDEs (with Samy Tindel) (in preparation)