My research interests lie at the frontier of large-scale continuous optimization. Nonconvexity, nonsmooth analysis, complexity bounds, and interactions with random matrix theory and high-dimensional statistics appear throughout work. Modern applications of machine learning demand these advanced tools and motivate me to develop theoretical guarantees with an eye towards immediate practical value. My current research program is concerned with developing a coherent mathematical framework for analyzing average-case (typical) complexity and exact dynamics of learning algorithms in the high-dimensional setting.