I am a fifth year graduate student at Michigan State University. I am currently on the job market! All of my research articles are on the arXiv, but you can also find them on my webpage. My research integrates analytic and geometric techniques to study evolutionary partial differential equations. More specifically, my research investigates global/finite-in-time existence properties to equations that model wave-like phenomena (i.e. relativistic membranes). The point of view I take is a perturbative one, where I take a fixed background solution and study its stability under small perturbations. My advisor is Willie Wong.
I am also working on a project with Jun Kitagawa and his graduate student Seonghyeon Jeong on regularity theory of generated Jacobian equations.
These are notes that I wrote to prepare for my comprehensive exam. They cover topics that range from the positive energy theorem, global existence for quasilinear wave equations, generalized solutions to the Monge-Ampère, and GWP to the defocussing nonlinear Schrödinger equation.