### Research Focus

Numerical analysis, scientific computing, and deep learning

I am interested in the study and development of numerical algorithms in applied mathematics. I mainly work in the following three areas: (1) Novel spectral methods for the solution of differential equations, (2) Low-rank techniques, and (3) Theoretical aspects of deep learning.

### Publications

Dense networks that do not synchronize and sparse ones that do (with M. Stillman and S. H. Strogatz), Chaos, 30 (2020), 083142.

Fast algorithms using orthogonal polynomials (with S. Olver and R. M. Slevinsky), Acta Numerica, 29 (2020), pp. 573-699.

Stable extrapolation of analytic functions (with L. Demanet), Foundations of Computational Mathematics, 19 (2019), pp. 297-331.

Bounds on the singular values of matrices with displacement structure (with B. Beckermann), SIAM Review, 61 (2019), pp. 319-344.

Why are big data matrices approximately low rank? (with M. Udell), SIAM Journal on Mathematics of Data Science, 1 (2019), pp. 144-160.

## In the news

- New center merges math, AI to push frontiers of science
- Arts and Sciences faculty featured on Academic Minute
- Weiss teaching award honors eight exceptional faculty
- Rational neural network advances machine-human discovery
- Six A&S professors named 2022 Simons fellows
- Computing with rational functions
- Eleven assistant professors win NSF early-career awards
- 30 Arts & Sciences faculty honored with endowed professorships
- Grants create engagement opportunities for students
- Grants create community-engaged opportunities for students
- Math professor mentors winner of science talent search

## MATH Courses - Fall 2023

- MATH 2940 : Linear Algebra for Engineers
- MATH 4900 : Supervised Research
- MATH 4901 : Supervised Reading
- MATH 7290 : Seminar on Scientific Computing and Numerics