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.

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Publications/Preprints

  1. 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", arXiv:2209.11027 (2022). arXiv
  2. J. Kaye, K. Chen, H.U.R. Strand, "libdlr: Efficient imaginary time calculations using the discrete Lehmann representation", Comput. Phys. Commun., 280 (2022), 108458. journal
  3. Y. Núñez-Fernández, M. Jeannin, P.T. Dumitrescu, T. Kloss, J. Kaye, O. Parcollet, X. Waintal, "Learning Feynman diagrams with tensor trains", arXiv:2207.06135 (2022). arXiv
  4. J. Kaye, K. Chen, O. Parcollet, "Discrete Lehmann representation of imaginary time Green's functions", Phys. Rev. B, 105 (2022), 235115. journal arXiv
  5. J. Kaye, A. Barnett, L. Greengard, "A high-order integral equation-based solver for the time-dependent Schrödinger equation", Comm. Pure Appl. Math., 75 (2022), 1657-1712. journal arXiv
  6. J. Kaye, H.U.R. Strand, "A fast time domain solver for the equilibrium Dyson equation", arXiv:2110.06120 (2021). arXiv
  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. Hoskins, J. Kaye, M. Rachh, J.C. Schotland, "A fast, high-order numerical method for the simulation of single-excitation states in quantum optics", arXiv:2109.06956 (2021). arXiv
  9. J. Kaye, D. Golež, "Low rank compression in the numerical solution of the nonequilibrium Dyson equation", SciPost Phys., 10 (4), 091 (2021). journal
  10. J. Kaye, L. Greengard, "A fast solver for the narrow capture and narrow escape problems in the sphere", J. Comput. Phys. X, 5 (2022), 100047. journal
  11. J. Kaye, L. Greengard, "Transparent boundary conditions for the time-dependent Schrödinger equation with a vector potential", arXiv:1812.04200 (2018). arXiv
  12. 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 (2016), 139-144. journal arXiv
  13. 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) (2015), 1741-1773. journal arXiv
  14. 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) (2014), 031006. 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

libdlr Efficient representation of imaginary time Green's functions using the Discrete Lehmann Representation

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