Alex Barnett

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 seek strong applicants for postdocs (FRF, due 12/15) and research scientists (Open Rank, due 1/15); please reach out if your work intersects my areas.

Many of my papers are on arXiv, most are in google scholar; also see outreach and education. Research and teaching pre-2018 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.

The numerical group at CCM seeks 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 many blockbuster sequels. I was an organizer for the tutorial workshop Computational Tools for PDEs in Complicated Geometries and Interfaces (2024), teaching boundary integral equations and other high-order solvers.

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

Recent research images/movies (older ones)

3D Stokes sedimentation (mobility) of 10000 rigid ellipsoids solved to 5-digit accuracy using one-body preconditioned method of fundamental solutions (with A. Broms and A.-K. Tornberg; arXiv '24).	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; JCP '24).	Point excitation of 2D infinite periodic sound-hard polygon to 10-digit accuracy, modeling dispersive trapped waves at Mayan pyramid staircases (with F. Agocs; JCP '24).

News, talk slides, and outreach

• FINUFFT v2.3 released with SIMD-enabled performance gains and switchable FFT. Our GPU code was just declared "the fastest NUFFT in the west, and by a wide margin" in MRI benchmarks at INRIA. We now offer type 3 transforms on the GPU. Recent work in large part due to Marco Barbone, with help from Libin Lu, Martin Reinecke, and our team, 9/19/24.
• FINUFFT is used to optimize up to a billion scatterer locations to give a desired spectral density or correlation, by NYU physicists: PRE paper, and Phys. Mag. article with movie, 9/13/24.
• Congratulations to postdoc mentee Fruzsina Agocs on moving to her new tenure-track job in computer science at CU Boulder, Fall 2024!
• My paper with Dhairya Malhotra on a convergent and efficient boundary integral scheme (CSBQ) for Stokes flow around slender bodies appeared in J. Comput. Phys.. This vastly improves on the use of slender body theory for numerical viscous hydrodynamics.
• A short observation on quadrature of high-frequency Sommerfeld integrals in markdown with MATLAB/Octave demo, 1/24/24.
• Software advice and nonuniform FFT tutorial talk given at Flatiron-Wide Autumn Meeting, 10/23/23.
• My paper with Fruzsina Agocs on adaptive Riccati defect correction for frequency-independent solution of oscillatory 2nd-order linear ODEs, was accepted by SINUM.
• See a blog-post style GitHub repo comparing two fast spectral methods for the Poisson equation in the square, with Dan Fortunato.
• Fruzsina Agocs presented a poster on our joint work on acoustic scattering and trapping on periodic surfaces (with applications to the raindrop effect at ancient Mayan staircases) at FACM23, NJIT, 5/26/23. Our paper appears in JCP in 2024.
• May 2023: Our paper on iterated quadrature for Brillouin zone integrals in quantum physics was accepted at SciPost Physics.
• April 2023: Congratulations to postdoc mentee Dan Fortunato on his ARS appointment at Flatiron, joint between CCB and CCM.
• Courant Institute (NYU), 11/11/22: Equispaced Fourier representations for efficient Gaussian process regression from a billion data points (submitted to SIAM/ASA J. Uncert. Quant.; analysis results to ACHA). Joint work with Philip Greengard, Manas Rachh. Also given at Dartmouth College, Yale, and Imperial College.
• May 2022: Postdoc mentee Fruzsina Agocs presented our joint work An adaptive spectral method for oscillatory second-order linear ODEs with frequency-independent cost (submitted to SIAM J. Numer. Anal.), at CMO (Oaxaca). She presented more recent versions at NJIT, Chicago, NYU, Yale, and SIAM CSE23. Check out her riccati Python package.
• CMO workshop (Oaxaca, Mexico), 5/26/22: Challenges in fast solvers for highly oscillatory problems (short overview).
• July 2022: Congratulations to former intern Yu-Hsuan (Melody) Shih [GH] on receiving her PhD at NYU and moving to a new job as a senior software engineer working on math libraries at nVidia.
• April 2022: Congratulations to postdoc mentee Jason Kaye on his ARS appointment at Flatiron, joint between CCQ and CCM.
• Flatiron-Wide Algorithms and Mathematics (FWAM3), 10/14/21: Joys and pitfalls of numerical computing (accompanying MATLAB/Octave demo codes: pisqsix.m, bigpca.m, stoch.m, linsys.m )
• SIAM Annual Meeting, online (minisymposium 57), 7/21/21: Fresnel diffraction for starshade design using the non-uniform FFT.
• ICOSAHOM, online (minisymposium 27a), 7/12/21: Quadrature by fundamental solutions: kernel-independent layer potential evaluation for large collections of simple objects. Work with David Stein (CCB).
• Congratulations to first author (and former CCM intern) Yu-hsuan (Melody) Shih for the Best Paper Award PDSEC-21 for our paper on cuFINUFFT. Here's her 20-min talk video.
• Congratulations to postdoc mentee Jun Wang on her tenure-track job in math at Tsinghua University.
• Our work on SpikeForest (paper) and spike sorting featured on the Neural Implant Podcast, thanks to Jeremy Magland and James Jun, 3/16/20.
• Princeton PACM Seminar, 2/3/20: Building a better non-uniform fast Fourier transform.
• Flatiron-Wide Algorithms and Mathematics (FWAM), 10/30/19: Introduction to interpolation, integration, and spectral methods (see Lecture I; lecture II by Keaton Burns).
• Mathematical Fluids, Materials and Biology, U. Michigan, 6/14/19: Fast boundary integral solvers for Stokes flows: quadrature, periodization, adaptivity.
• SIAM CSE, Spokane, WA, 3/1/19: Overview of high-order Nyström surface quadratures for fast solvers (review talk).
• Random geometries / Random topologies, ETH Zürich, 12/4/17: Experimental Nazarov-Sodin constants, genus, and percolation on nodal domains for 2D and 3D random waves (given remotely to save CO₂).

Other links

• Events at CCM Flatiron this week, and all of Flatiron this month.
• Flatiron SciWare tutorials on programming, tools, software dev.
• Flatiron Institute cluster wiki (SCC).
• FI latex beamer templates repo.
• Some numerical analysis seminars: One World (Edinburgh), Sayas (UMD), E-NLA, CMSC (CIMS).
• My father Ross was also a computational physicist.
• Check out The Arts Oasis created by my wife, Liz Canner.