Alex Barnett

Local resources

Welcome! Here is my CV, a bio, and below is some news.

To find out about my research and contact details, and research of colleagues, see the Center for Computational Mathematics, Flatiron Institute, Simons Foundation, and the Numerical Analysis area. Research topics at CCM include signal processing, numerical PDE, numerical analysis, fast algorithms, biophysics, fluids, waves, data analysis, computational statistics, deep learning, sampling, optimization, protein imaging, inverse problems, quantum simulation, neuroscience tools, and software libraries. We accept postdoc (FRF) applications each Fall.

Many of my papers are on arXiv, most are in google scholar; also see outreach and education. Research and teaching pre-2017 is also listed in a local copy of my former academic page as a professor of mathematics at Dartmouth College. You can find some of my numerical software projects on github and on CCM's software page.

I am an organizer for the June 10-14, 2024, tutorial workshop Computational Tools for PDEs in Complicated Geometries and Interfaces, which will teach boundary integral equations and other solver methods. Energetic numerical students and postdocs please apply!

I encourage high-quality submissions to the journal Advances in Computational Mathematics (ACOM), for which I am co-Editor in Chief with Karsten Urban. I was a guest editor for this topical collection on integral equations. In 2019 I was the main organizer for Flatiron-Wide Algorithms and Mathematics (FWAM) which had three similar blockbuster sequels.

Meetings: Wednesdays at 10am we have the CCM Colloquium / Group Meeting. Tuesdays at 10am we have Scientific Computing Seminar.

Recent research images/movies

Some images click to play movie (MP4)... or see old Dirichlet Laplace eigenfunctions (|φj|2 for half-mushroom, quarter-stadium)
3D Stokes flow lines solved near slender rigid bodies separated by 1/20 of their minor radius, computed to 10-digit accuracy using CSBQ (with D. Malhotra; arxiv '23). Timings of our ARDC solver vs others, for a 2nd-order oscillatory ODE with frequency λ, via adaptive defect correction for the Riccati phase function (with F. Agocs; SINUM '23) 2D periodic rheology simulation via boundary integral equations: 25 rigid neutrally-buoyant ellipses per unit cell in a shearing Stokes flow (with J. Wang, E. Nazockdast; JCP '21)

News, talk slides, and outreach

Other links