My research is in pure, applied, and computational harmonic analysis, motivated in large part by a desire to rigorously understand the mathematical underpinnings of machine learning algorithms. This understanding in turn leads to the development of new machine learning paradigms, particularly for the analysis of high dimensional data. Finally, these methods are leveraged to open up new avenues for scientific breakthroughs, either by circumventing prohibitively costly computations or by revealing unforeseen patterns in complex data.
My primary interests range over pure and applied topics, but can be loosely summarized as:
- Wavelet theory, particularly how it relates to deep learning (scattering transforms)
- Diffusion based manifold learning
- Smooth extensions and interpolations of Whitney type
- Quantum chemistry and many body problems
- Applications in bio-medical data analysis