Research

My research combines analysis, algorithms, and computation. Much of it is driven by the question: how can we design methods that are both mathematically principled and genuinely useful for large-scale scientific problems?

Main areas

Spectral methods and numerical analysis

I work on high-accuracy computational methods for differential equations, approximation by functions, and fast transforms. This includes spectral and ultraspherical methods, eigenvalue problems for differential operators, and fast polynomial transforms.

Low-rank approximation and randomized linear algebra

Many problems in scientific computing and data analysis are governed by hidden low-rank structure. I am interested in algorithms and theory for matrix recovery, tensor decompositions, sketching methods, and structured approximation.

Mathematics of deep learning and operator learning

A recurring theme in my recent work is the mathematical analysis of learning problems motivated by PDEs and operators. This includes learning Green’s functions, operator learning without adjoints, rational neural networks, and other mathematically interpretable approaches to machine learning.

Dynamical systems

I also work on problems related to synchronization, Koopman operators, and nonlinear dynamics, often in collaboration with researchers in applied mathematics and physics.

For prospective students

Graduate students interested in working with me are welcome to send me an email. For undergraduate students, I usually look for a commitment of about 18 months and prefer students who are in their second or third year. To get a sense of my current interests, browse my recent papers.