My current research interests lie in the intersection of harmonic analysis and matrix analysis, and their diverse uses in applied problems such as quantum tomography, speech recognition, radar reconstruction, and machine learning. My work thus far has centered on frame theory and Lipschitz analysis a la Kirszbraun, but has also brought to bear key ideas from differential geometry and the theory of analytic varieties (Whitney stratifications) in order to understand the phase retrieval problem in the case of impure states. I am also interested in the use of Lipschitz analysis and differential geometry to understand and improve generative models in machine learning as well as in the theory (and applications to signal processing) of higher order Fourier analysis.