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The geometry and metric structure of data
How faithfully can we represent complex data with simple geometric structure — trees, hyperbolic spaces, and metric spaces — and what goes wrong when we cannot?
Machine learning for the physical and life sciences
Using machine learning to accelerate scientific discovery — from predicting metallic glasses to selecting markers in single-cell genomics.
Privacy, sparse recovery, and inverse problems
Recovering signals from few measurements while respecting constraints such as differential privacy, and solving nonlinear inverse problems.
Foundations of sparse approximation
The mathematical foundations underpinning my applied work: sparse approximation, sublinear-time and sparse Fourier algorithms, and compressive sensing.