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 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 pre2017 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 1014, 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 highquality submissions to the journal Advances in Computational Mathematics (ACOM),
for which I am coEditor 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 FlatironWide 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 (φ_{j}^{2} for halfmushroom, quarterstadium)



3D Stokes flow lines solved near slender rigid bodies separated by 1/20 of their minor radius, computed to 10digit accuracy using CSBQ (with D. Malhotra; arxiv '23).

Timings of our ARDC solver vs others,
for a 2ndorder 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 neutrallybuoyant ellipses per unit cell in a shearing Stokes flow (with J. Wang, E. Nazockdast; JCP '21)

News, talk slides, and outreach
 Congratulations to postdoc mentee
Fruzsina Agocs
on being accepted to this year's Rising Stars in Computational and Data Sciences workshop.
 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 as a numerical tool.
 A short observation on quadrature of highfrequency Sommerfeld integrals in markdown with MATLAB/Octave demo, 1/24/24.
 Software advice and nonuniform FFT tutorial talk given at FlatironWide Autumn Meeting, 10/23/23.
 My paper with
Fruzsina Agocs
on adaptive Riccati defect correction for frequencyindependent solution of oscillatory 2ndorder linear ODEs, was accepted by SINUM.
 See a blogpost 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.
 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 secondorder linear ODEs with frequencyindependent 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 YuHsuan (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.

FlatironWide 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 nonuniform FFT.
 ICOSAHOM, online (minisymposium 27a), 7/12/21: Quadrature by fundamental solutions: kernelindependent layer potential evaluation for large collections of simple objects. Work with David Stein (CCB).
 Congratulations to first author (and former CCM intern) Yuhsuan (Melody) Shih for the Best Paper Award PDSEC21 for our paper on cuFINUFFT. Here's her 20min talk video.
 Congratulations to postdoc mentee Jun Wang on her tenuretrack 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 nonuniform fast Fourier transform.
 FlatironWide 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 highorder Nyström surface quadratures for fast solvers (review talk).
 Random geometries / Random topologies, ETH Zürich, 12/4/17:
Experimental NazarovSodin constants, genus, and percolation on nodal domains for 2D and 3D random waves
(given remotely to save CO_{2}).
Other links