Jason Kaye

Flatiron Research Fellow
Center for Computational Mathematics
Center for Computational Quantum Physics
Flatiron Institute

[email protected]
Curriculum Vitae

Research Interests:

My research focuses on the development of robust, high-order, and scalable numerical algorithms for problems in computational physics, and primarily 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. As such, most of my projects involve close collaborations with physicists, and cover both algorithm development and implementation for use by practitioners.


Dissertation: Integral equation-based numerical methods for the time-dependent Schrödinger equation
Adviser: Dr. Leslie Green​gard


libdlr: Efficient imaginary time calculations using the discrete Lehmann representation 
J. Kaye, H.U.R. Strand
arXiv:2110.06765 (2021)

A fast time domain solver for the equilibrium Dyson equation
J. Kaye, H.U.R. Strand
arXiv:2110.06120 (2021)

Analysis of single-excitation states in quantum optics
J. Hoskins, J. Kaye, M. Rachh, J.C. Schotland
arXiv:2110.07049 (2021)

A fast, high-order numerical method for the simulation of single-excitation state in quantum optics
J. Hoskins, J. Kaye, M. Rachh, J.C. Schotland
arXiv:2109.06956 (2021)

Discrete Lehmann representation of imaginary time Green's functions
J. Kaye, K. Chen, O. Parcollet
arXiv:2107.13094 (2021)

Low rank compression in the numerical solution of the nonequilibrium Dyson equation
J. Kaye, D. Golež
SciPost Phy​​​s.​ 10 (4), 091 (2021) (open access) 

A high-order integral equation-based solver for the time-dependent Schrödinger equation
J. Kaye, A. Barnett, L. Greengard
Commun. Pure Appl. Math (2020) 

A fast solver for the narrow capture and narrow escape problems in the sphere
J. Kaye, L. Greengard
J. Comput. Phys. X 5, 100047 (2020) (open access)

Transparent boundary conditions for the time-dependent Schrödinger equation with a vector potential
J. Kaye, L. Greengard
arXiv:1812.04200 (2018)

A Gaussian-like immersed-boundary kernel with three continuous derivatives and improved translational invariance
Y. Bao, J. Kaye, C. S. Peskin
J. Comput. Phys. 316, 139-144 (2016)

A posteriori error estimator for adaptive local basis functions to solve Kohn-Sham density functional theory
J. Kaye, L. Lin, C. Yang
Commun. Math. Sci. 13 (7), 1741-1773 (2015)

Fast prediction and evaluation of gravitational waveforms using surrogate models
S. E. Field, C. R. Galley, J. S. Hesthaven, J. Kaye, M. Tiglio
Phys. Rev. X 4 (3), 031006 (2014) (open access)