Jason Kaye

I am an Associate Research Scientist, joint between the Center for Computational Mathematics and the Center for Computational Quantum Physics at the Flatiron Institute. My research focuses on the development of robust, high-order, and scalable numerical algorithms for problems in computational quantum physics. I work with tools involving the numerical solution of partial differential equations and integral equations, high-order methods, and fast algorithms for the compression and application of structured operators.

I place an emphasis on developing practical algorithms to address specific bottlenecks faced by computational scientists. Most of my projects involve close collaborations with physicists, and cover algorithm development, implementation, and software.

Download my CV (Feb '23)

Publications/Preprints

(ordered by first appearance)
If no arXiv link is given, journal publication is open access.

  1. H. LaBollita, J. Kaye, A. Hampel, "Stabilizing the calculation of the self-energy in dynamical mean-field theory using constrained residual minimization", arXiv:2310.01266 (2023). arXiv
  2. J. Kaye, H. U. R. Strand, D. Golež, "Decomposing imaginary time Feynman diagrams using separable basis functions: Anderson impurity model strong coupling expansion", arXiv:2307.08566 (2023). arXiv
  3. N. Sheng, A. Hampel, S. Beck, O. Parcollet, N. Wentzell, J. Kaye, K. Chen, "Low-rank Green's function representations applied to dynamical mean-field theory", Phys. Rev. B., 107, 245123 (2023). journal arXiv
  4. J. Kaye, S. Beck, A. Barnett, L. Van Muñoz, O. Parcollet, "Automatic, high-order, and adaptive algorithms for Brillouin zone integration", SciPost Phys., 15 (2), 062 (2023). journal
  5. J. Kaye, A. Barnett, L. Greengard, U. De Giovannini, A. Rubio, "Eliminating artificial boundary conditions in time-dependent density functional theory using Fourier contour deformation", J. Chem. Theory Comput., 19 (5), 1409-1420 (2023). journal arXiv
  6. Y. Núñez-Fernández, M. Jeannin, P. T. Dumitrescu, T. Kloss, J. Kaye, O. Parcollet, X. Waintal, "Learning Feynman diagrams with tensor trains", Phys. Rev. X, 12, 041018 (2022). journal
  7. J. Hoskins, J. Kaye, M. Rachh, J. C. Schotland, "Analysis of single-excitation states in quantum optics", arXiv:2110.07049 (2021). arXiv
  8. J. Kaye, K. Chen, H. U. R. Strand, "libdlr: Efficient imaginary time calculations using the discrete Lehmann representation", Comput. Phys. Commun., 280, 108458 (2022). journal
  9. J. Kaye, H. U. R. Strand, "A fast time domain solver for the equilibrium Dyson equation", Adv. Comput. Math., 49, 63 (2023). journal
  10. J. Hoskins, J. Kaye, M. Rachh, J. C. Schotland, "A fast, high-order numerical method for the simulation of single-excitation states in quantum optics", J. Comput. Phys., 473, 111723 (2023). journal arXiv
  11. J. Kaye, K. Chen, O. Parcollet, "Discrete Lehmann representation of imaginary time Green's functions", Phys. Rev. B, 105, 235115 (2022). journal arXiv
  12. J. Kaye, D. Golež, "Low rank compression in the numerical solution of the nonequilibrium Dyson equation", SciPost Phys., 10 (4), 091 (2021). journal
  13. J. Kaye, A. Barnett, L. Greengard, "A high-order integral equation-based solver for the time-dependent Schrödinger equation", Comm. Pure Appl. Math., 75, 1657-1712 (2022). journal arXiv
  14. J. Kaye, L. Greengard, "A fast solver for the narrow capture and narrow escape problems in the sphere", J. Comput. Phys. X, 5, 100047 (2020). journal
  15. J. Kaye, L. Greengard, "Transparent boundary conditions for the time-dependent Schrödinger equation with a vector potential", arXiv:1812.04200 (2018). arXiv
  16. Y. Bao, J. Kaye, C. S. Peskin, "A Gaussian-like immersed-boundary kernel with three continuous derivatives and improved translational invariance", J. Comput. Phys., 316, 139-144 (2016). journal arXiv
  17. J. Kaye, L. Lin, C. Yang, "A posteriori error estimator for adaptive local basis functions to solve Kohn-Sham density functional theory", Commun. Math. Sci., 13 (7), 1741-1773 (2015). journal arXiv
  18. S. E. Field, C. R. Galley, J. S. Hesthaven, J. Kaye, M. Tiglio, "Fast prediction and evaluation of gravitational waveforms using surrogate models", Phys. Rev. X, 4 (3), 031006 (2014). journal
Dissertation: Integral equation-based numerical methods for the time-dependent Schrödinger equation (Courant Institute of Mathematical Sciences, New York University, Adviser: Leslie Greengard)


Software

cppdlr C++ library implementing the discrete Lehmann representation of imaginary time Green's functions
libdlr Python & Fortran libraries implementing the discrete Lehmann representation of imaginary time Green's functions (see also the libdlr companion paper)
AutoBZ Julia library implementing algorithms for automatic, high-order, and adaptive Brillouin zone integration (code written by Lorenzo van Muñoz)

Contact