I have worked in a number of areas, including Complex Analysis, Continuum Mechanics, General Relativity, Numerical Analysis, Quantum Mechanics, Partial Differential Equations and Special Functions. For the past few years I have been principally concerned with systems of hyperbolic partial differential equations, especially those systems which are of particular physical interest--mostly the Einstein equations of General Relativity, but also the Euler equations of Fluid Mechanics and the equations governing Nonlinear Elasticity.

Excellent overviews of General Relativity, in varying levels of detail, are available from Muppet Labs and Living Reviews.

  1. The massless Boltzmann equation in Minkowski spacetime with Ho Lee , Ernesto Nungesser , and Paul Tod , , 2026,
  2. Homogeneous solutions to the Einstein-matter equations with a magnetic field and a conformal gauge singularity with Ho Lee , Ernesto Nungesser , and Paul Tod , Revista Matemática Complutense, 2025,
  3. Well-posedness of anisotropic and homogeneous solutions to the Einstein-Boltzmann system with a conformal gauge singularity with Ho Lee , Ernesto Nungesser , and Paul Tod , Journal of Differential Equations, ,
  4. On almost Ehlers–Geren–Sachs theorems with Ho Lee and Ernesto Nungesser , Classical and Quantum Gravity, 2022
  5. A lower bound for the amplitude of traveling waves of suspension bridges with Paschalis Karageorgis , Nonlinear Analysis , 2012
  6. Sharp bounds on 2m/r for static spherical objects with Paschalis Karageorgis , Classical and Quantum Gravity , 2008
  7. A compactness criterion for real plane algebraic curves , Forum Mathematicum , 2007
  8. Strichartz estimates for the Wave and Schrödinger Equations with Potentials of Critical Decay with N. Burq , F. Planchon , and A.S. Tahvildar-Zadeh , Indiana Journal of Mathematics, 2004
  9. Scalar waves on a naked-singularity background with A.S. Tahvildar-Zadeh , Classical and Quantum Gravity, 2004
  10. Strichartz estimates for the Wave and Schrödinger Equations with the Inverse-Square Potential , with N. Burq , F. Planchon , and A.S. Tahvildar-Zadeh , Journal of Functional Analysis, 2003
  11. Dispersive estimate for the wave equation with the inverse-square potential , with F. Planchon , and A.S. Tahvildar-Zadeh , Discrete and Continuous Dynamical Systems, 2003
  12. Lp estimates for the wave equation with the inverse-square potential , with F. Planchon , and A.S. Tahvildar-Zadeh , Discrete and Continuous Dynamical Systems, 2003
  13. On Hubbell's rectangular source integral , Radiation Physics and Chemistry, 2001
  14. An essentially singular classical limit , Advances in Mathematics, 1999
  15. Singular perturbation series in quantum mechanics , Advances in Mathematics, 1999
  16. A convergence speeding algorithm with applications to numerical integration , Advances in Applied Mathematics, 1999
  17. Complex Analysis, Fundamentals of the Classical Theory of Functions , Birkhäuser, 1998
  18. Automorphic functions on general domains in Cn , Duke Mathematics Journal, 1996
  19. Hölder and Lp Estimates for ðb on Domains of Finite Type , Doctoral Thesis, Princeton University 1993