Grand Teton Grand Canyon of the Yellowstone Snowy Range

research interests

Applied analysis and partial differential equations: nonlinear waves, existence & stability of traveling waves, Evans-function techniques, conservation & balance laws, gas dynamics, shock waves, combustion, integrable equations.

recent preprint(s)

  • Analysis and development of compact finite difference schemes with optimized numerical dispersion relations (with Yi-Hung Kuo and Long Lee), arXiv:1409.3535.
  • Semiclassical soliton ensembles for the focusing nonlinear Schrödinger equation: recent developments, Preprint, 2013 (accepted for publication in Contemporary Mathematics).
  • Viscous hyperstabilization of detonation waves in one space dimension (with Blake Barker, Jeffrey Humpherys, and Kevin Zumbrun), arXiv:1311:6417.
  • The WKB approximation of semiclassical eigenvalues of the Zakharov-Shabat problem (with Yeongjoh Kim and Long Lee), arXiv:1310.4145 (The published version has appeared in the Journal of Mathematical Physics).
  • Stability of viscous weak detonation waves for Majda's model (with Jeffrey Hendricks, Jeffrey Humpherys, and Kevin Zumbrun), arXiv:1307.4416.
  • Stability of viscous detonations for Majda's model (with Jeffrey Humpherys and Kevin Zumbrun), arXiv:1301.1260 (The published version has appeared in Physica D).
  • A second look at the Gaussian semiclassical soliton ensemble for the focusing nonlinear Schrödinger equation (with Long Lee), arXiv:1211.1988 (The published version has appeared in Physics Letters A).

selected publications

about me

I grew up in Fort Wayne, Indiana (the one-time magnet wire capital of the world), and I earned a BA in mathematics from St. Olaf College. My PhD is from Indiana University, Bloomington. After a post-doctoral stint at the University of Michigan, I came to Wyoming in 2005. Outside of mathematics, I enjoy skiing, ruminating on the New York Times crossword puzzle, drinking good coffee, and passionately following the (mis)fortunes of the Indiana University men's basketball team.