I am an Associate Professor at Michigan State University in the College of Natural Science and the College of Engineering. I have a joint appointment between the Department of Computational Mathematics, Science and Engineering and the Department of Mathematics, and I am also a member of the Center for Quantum Computing, Science & Engineering. At MSU I am the scientific leader of the ComplEx Data Analysis Research (CEDAR) team.
My research interests are in developing machine learning algorithms for the analysis of high dimensional data. I like to develop new algorithms with mathematically provable guarantees, in addition to using these algorithms to push the state of the art in fields such as quantum chemistry, materials science and biomedicine, amongst others. The underlying mathematics is rooted in harmonic analysis, with contributions from spectral graph theory, geometry, statistics, and theoretical computer science. A common theme in much of my work is the use multi-scale data decompositions that leverage priors, symmetries, invariants, and related properties inherent to the problem at hand.
My primary interests by group are:
- Mathematical foundations of deep learning
- Geometric methods for high dimensional data analysis
- Smooth extension and interpolation of data, with efficient algorithms (Whitney-type extensions)
- Multi-reference alignment inverse problems
- Machine learning and quantum many body physics
- Biological data analysis
Before arriving at Michigan State University, I was a Postdoctoral Researcher working in the Département d’Informatique at the École normale supérieure in Paris, France, where I was part of Stéphane Mallat’s Data Team. Prior to that appointment I was a Postdoctoral Associate working with Ronald Coifman in the Department of Mathematics at Yale University. I spent the two months between those appointments running an NSF Research Experience for Undergraduates (REU) in the Department of Mathematics at Cornell University on high dimensional data analysis.
I received my PhD in Mathematics from the University of Maryland. My advisors were John Benedetto and Kasso Okoudjou. I was also part of the Norbert Weiner Center for Harmonic Analysis and Applications while at Maryland. I obtained my BA in Mathematics from Cornell University, under the supervision of Robert Strichartz.