Research Interests
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:
- Mathematical foundations of deep learning
(scattering transforms, convolutional neural networks, generative models)
- Machine learning and multiscale physics
(quantum chemistry, materials science, turbulence)
- Geometric and graphical models for high dimensional data analysis
(manifold learning, graph learning, geometric deep learning, biomedical data)
- Smooth extension, interpolation, and regression of data, with efficient algorithms
(Whitney extensions, statistical learning theory)
