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.
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.