My main areas of expertise include dispersive and fluid equations, functional analysis, order structures, and phase retrieval. In PDE, I have worked on nonlinear Schrödinger equations, free boundary Euler equations, and magnetohydrodynamics. In functional analysis, I began by studying the various connections between minimal topologies, unbounded topologies, uo-convergence and universal completions. More recently, I have focused on metric properties of function spaces, e.g., free Banach lattices, positive bases, and subspace structure. Finally, I have done some work in approximation theory and signal processing; more specifically, on stable phase retrieval, frame theory, and greedy algorithms.