ABOUT ME

I am a Hermann-Weyl instructor as well an ETH fellow at ETH Zurich. Before this, I completed my PhD at UC Berkeley working under the supervision of Daniel Tataru. My main areas of expertise include dispersive and fluid equations, functional analysis, order structures, spectral theory and phase retrieval. In PDE, I have worked on nonlinear Schrödinger equations, free boundary Euler equations, magnetohydrodynamics and the hot spots conjecture. 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, subspace structure, maximal inequalities and connections to harmonic analysis and descriptive set theory. Finally, I have made several contributions to approximation theory and signal processing; more specifically, on stable phase retrieval, frame theory, saturation recovery, unlimited sampling and greedy algorithms.