Sep 2023 - Aug 2024 | Visiting Scholar | CCM, Flatiron Institute | Sep 2020 - | Associate Professor of Mathematics | Courant Institute, NYU |
Sep 2018 - Aug 2019 | Visiting Assistant Professor of Mathematics | MIT |
Sep 2014 - Aug 2020 | Assistant Professor of Mathematics | Courant Institute, NYU |
Sep 2012 - Aug 2014 | Courant Instructor | Courant Institute, NYU |
Sep 2010 - Aug 2012 | Associate Research Scientist | Courant Institute, NYU |
Aug 2007 - Jul 2020 | Quant Researcher / Assistant Trader | Susquehanna International Group, LLP |
Dec 2007 | PhD Applied Mathematics | Yale University |
May 2003 | AB Mathematics | Cornell University |
Paul Beckman
Annie Liu
Amandin Rabeendran
Paco Rilloraza
Bahram Khalichi (UC Berkeley)
Sam
Potter (Coreform)
Tristan Goodwill (U. Chicago)
Evan Toler (Argonne)
Dhairya
Malhotra (Flatiron Institute)
Yuwei Jiang (Plus)
Daria
Sushnikova (KAUST)
Sunli Tang (Uber)
Please contact me for more info.
Collaborators
Alex
Barnett (Flatiron)
Antoine Cerfon (NYU)
Charlie Epstein (UPenn)
Zydrunas Gimbutas (NIST)
Leslie Greengard (NYU)
Philip Greengard (Columbia)
David W. Hogg (NYU)
Lise-Marie Imbert-Gerard (Arizone)
Andreas Klöckner (UIUC)
Jun Lai
(Zhejiang)
Manas
Rachh (Flatiron)
Felipe
Vico (Valencia)
High-fidelity fast algorithms for inverse problems
and imaging in three dimensions O'Neil (PI) and Borges (PI, UCF), Office of Naval Research Award #N00014-21-1-2383, 9/1/21 - 8/31/24 |
Hidden Symmetries and Fusion Energy A. Bhattacharjee (PI), Cerfon (Co-I), O'Neil (Co-I), et. al., Simons Foundation, 6/1/18 - 5/31/22 |
Multi-level randomized algorithms for high-frequency
wave propagation Greengard (PI) and O'Neil (Co-I), Office of Naval Research Award #N00014-18-1-2307, 6/1/18 - 5/31/22 |
Toward real-time electromagnetic design: Fast,
accurate, and robust integral equation-based
solvers O'Neil (PI), Office of Naval Research Award #N00014-17-1-2451, 6/1/17 - 5/31/20 |
Fast high-order CAD-compatible Nystrom methods for
frequency domain electromagnetics O'Neil (PI), Office of Naval Research Award #N00014-17-1-2059, 1/1/17 - 12/31/19 |
An integral equation-based solver for the
Laplace-Beltrami operator on triangulated
surfaces O'Neil (PI), Office of Naval Research Award #N00014-15-1-2669, 7/1/2015 - 6/30/2016 |
Fast analysis-based computational methods for
statistics O'Neil (PI), AIG NYU-AIG Partnership on Innovation for Global Resilience, 9/1/2014 - 8/31/2015 |
On the construction of scattering matrices for
irregular or elongated enclosures using Green’s
representation formula C. Borges, L. Greengard, M. O'Neil, and M. Rachh. J. Sci. Comput., to appear. arXiv:2408.02881 |
A parametrix method for elliptic
surface PDEs T. Goodwill and M. O'Neil, arXiv.org > math.NA > 2401.12501, 2024. arXiv:2401.12501 |
Fast adaptive high-order integral
equation methods
for electromagnetic scattering from smooth
perfect electric
conductors F. Vico, L. Greengard, M. O'Neil, and M. Rachh, arXiv.org > math.NA > 2306.04473, 2023. arXiv:2306.04473 |
An interface formulation of the Laplace-Beltrami
problem on piecewise smooth surfaces T. Goodwill M. O'Neil, SIAM J. Math. Anal., 55(6): 7575-7615, 2023. journal arXiv:2108.08959 |
FMM-LU: A fast direct solver for
multiscale boundary integral equations in
three
dimensions D. Sushnikova, L. Greengard, M. O'Neil, and M. Rachh, SIAM Multiscale Model. Simul., 21(4): 1570-1601, 2023. journal arXiv:2201.07325 |
FMM-accelerated solvers for the
Laplace-Beltrami problem on complex surfaces in three
dimensions D. Agarwal, M. O'Neil, and M. Rachh, J. Sci. Comput., 97:25, 2023. journal (open-access) |
Efficient reduced-rank methods for
Gaussian processes with eigenfunction
expansions P. Greengard and M. O'Neil, Stat. Comput., 32:94, 2022. journal (open-access) |
Fast multipole methods for the evaluation
of layer potentials with locally-corrected
quadratures L. Greengard, M. O'Neil, M. Rachh, and F. Vico, J. Comput. Phys.: X, 10:100092, 2021. journal (open-access) |
A fast boundary integral method for
high-order multiscale mesh generation F. Vico, L. Greengard, M. O'Neil, and M. Rachh, SIAM J. Sci. Comput., 42(2):A1380-A1401, 2020. journal arXiv:1909.13356 |
Efficient high-order singular quadrature
schemes in magnetic fusion D. Malhotra, A. J. Cerfon, M. O'Neil, and E. Toler, Plasma Phys. Control. Fusion, 62(2):024004, 2019. journal arXiv:1909.07417 |
Taylor States in Stellarators: A Fast
High-order Boundary Integral Solver D. Malhotra, A. J. Cerfon, L.-M. Imbert-Gerard, and M. O'Neil, J. Comput. Phys., 397:108791, 2019. journal arXiv:1902.01205 |
An FFT-accelerated direct solver for
electromagnetic scattering from penetrable
axisymmetric objects J. Lai and M. O'Neil, J. Comput. Phys., 390:152-174, 2019. journal arXiv:1810.07067 |
A high-order wideband direct
solver for electromagnetic scattering
from bodies of revolution C. L. Epstein, L. Greengard, and M. O'Neil, J. Comput. Phys., 387:205-229, 2019. journal arXiv:1708.00056 |
Second-kind integral equations for the
Laplace-Beltrami problem on surfaces
in three dimensions M. O'Neil, Adv. Comput. Math., 44(5): 1385-1409, 2018. journal (open-access) |
A new hybrid integral representation for
frequency domain scattering in layered media J. Lai, L. Greengard, and M. O'Neil, Appl. Comput. Harm. Anal., 45(2):359-378, 2018. journal arXiv:1507.03491 |
An integral equation-based numerical
solver for Taylor states in toroidal
geometries M. O'Neil and A. Cerfon, J. Comput. Phys., 359:263-282, 2018. journal arXiv:1611.01420 |
Accurate and efficient numerical
calculation of stable densities
via optimized quadrature and asymptotics S. Ament and M. O'Neil, Stat. Comput., 28(1):171-185, 2017. journal (open-access) |
Fast algorithms for Quadrature by
Expansion I: Globally valid expansions M. Rachh, A. Klöckner, and M. O'Neil, J. Comput. Phys., 345:706-731, 2017. journal arXiv:1602.05301 |
Robust integral formulations for
electromagnetic scattering from three-dimensional
cavities J. Lai, L. Greengard, and M. O'Neil, J. Comput. Phys., 345:1-16, 2017. journal arXiv:1606.03599 |
Fast symmetric factorization of
hierarchical matrices with
applications S. Ambikasaran, M. O'Neil, and K. R. Singh, technical report, 2016. arXiv:1405.0223 |
Smoothed corners and scattered
waves C. L. Epstein and M. O'Neil, SIAM J. Sci. Comput., 38(5):A2665-A2698, 2016. journal arXiv:1506.08449 |
Fast Direct Methods for Gaussian
Processes S. Ambikasaran, D. Foreman-Mackey, L. Greengard, D. W. Hogg, and M. O'Neil, IEEE Trans. Pattern Anal. Mach. Intell., 38(2):252-265, 2016. journal arXiv:1403.6015 |
Debye Sources, Beltrami Fields, and a Complex
Structure on Maxwell Fields C. L. Epstein, L. Greengard, and M. O'Neil, Comm. Pure Appl. Math. 68(12):2237-2280, 2015. journal arXiv:1308.5425 |
Exact axisymmetric Taylor states for
shaped plasmas A. Cerfon and M. O'Neil, Phys. Plasmas 21, 064501, 2014. journal arXiv:1406.0481 |
A generalized Debye source approach to electromagnetic
scattering in layered
media M. O'Neil, J. Math. Phys. 55, 012901, 2014. journal arXiv:1310.4241 |
On the efficient representation of the
impedance Green's function for the Helmholtz
equation M. O'Neil, L. Greengard, and A. Pataki, Wave Motion 51(1):1-13, 2014. journal arXiv:1109.6708 |
Quadrature by Expansion: A New Method for
the Evaluation of Layer
Potentials A. Klöckner, A. Barnett, L. Greengard, and M. O'Neil, J. Comput. Phys. 252:332-349, 2013. journal arXiv:1207.4461 |
A fast, high-order solver for the
Grad-Shafranov equation A. Pataki, A. J. Cerfon, J. P. Freidberg, L. Greengard, and M. O'Neil, J. Comput. Phys. 243:28-45, 2013. journal arXiv:1210.2113 |
A consistency condition for the vector potential in
multiply-connected domains C. L. Epstein, Z. Gimbutas, L. Greengard, A. Klöckner, and M. O'Neil, IEEE Trans. Magn. 49(3):1072-1076, 2013. journal arXiv:1203.3993 |
Debye sources and the numerical solution of the time
harmonic Maxwell equations, II C. L. Epstein, L. Greengard, and M. O'Neil, Comm. Pure Appl. Math. 66(5):753-789, 2013. journal arXiv:1105.3217 |
An algorithm for the rapid evaluation of special
function transforms M. O'Neil, F. Woolfe, and V. Rokhlin, Appl. Comput. Harmon. Anal. 28(2):203-226, 2010. journal |
Slow passage through resonance in Mathieu's
equation L. Ng, R. H. Rand, and M. O'Neil, J. Vib. Control 9(6):685-707, 2003. journal |
Semester | Number | Title |
---|---|---|
Fa 2024 | MA 4204 | Ordinary Differential Equations |
Sp 2023 | MATH 396 | Honors numerical analysis |
Fa 2022 | MATH 2011 | Computational electromagnetics |
Sp 2022 | MATH 2012 | Randomized numerical linear algebra |
Sp 2022 | MATH 396 | Honors numerical analysis |
Fa 2021 | MA 6973 | Computational statistics |
Sp 2021 | MA 6963 | Statistics |
Fa 2020 | MATH 2011 | Fast solvers |
Fa 2020 | MATH 233 | Theory of probability |
Sp 2020 | MA 4424 | Numerical analysis |
Fa 2019 | MATH 262 | Ordinary differential equations |
Sp 2019 | MATH 2840 | Computational methods for integral equations |
Sp 2018 | MATH 252 | Numerical analysis |
Fa 2017 | MATH 2011 | Integral equations and fast algorithms |
Fa 2016 | MA 2034 | Linear algebra and differential equations |
Sp 2016 | MA 4423 | Introductory numerical analysis |
Fa 2015 | MATH 2830 | Fast analysis-based algorithms |
Sp 2015 | MA 4423 | Introductory numerical analysis |
Fa 2014 | DS 1006 | Capstone project in Data Science |
Sp 2014 | MATH 234 | Mathematical statistics |
Fa 2013 | MATH 2011 | Data Science Projects |
Sp 2013 | MATH 234 | Mathematical statistics |
Fa 2012 | MATH 140 | Linear Algebra |
Sp 2012 | MATH 140 | Linear Algebra |