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.
- Multidimensional stability of large-amplitude Navier-Stokes shocks (with Jeffrey Humpherys and Kevin Zumbrun), arXiv:1603.03955.
- Analysis and development of compact finite difference schemes with optimized numerical dispersion relations (with Yi-Hung Kuo and Long Lee), arXiv:1409.3535.
recent & selected publications
- Semiclassical soliton ensembles for the focusing nonlinear Schrödinger equation: recent developments, in "Nonlinear Wave Equations: Analytic and Computational Techniques," 91 - 108, Contemporary Mathematics, 635, American Mathematical Society, Providence, RI, 2015.
- Viscous hyperstabilization of detonation waves in one space dimension (with Blake Barker, Jeffrey Humpherys, and Kevin Zumbrun), SIAM Journal on Applied Mathematics, 75 (2015): 885 - 906.
- Stability of viscous weak detonation waves for Majda's model (with Jeffrey Hendricks, Jeffrey Humpherys, and Kevin Zumbrun), Journal of Dynamics and Differential Equations, 27 (2015): 237 - 260.
- The Wentzel-Kramers-Brillouin approximation of semiclassical eigenvalues of the Zakharov-Shabat problem (with Yeongjoh Kim and Long Lee), Journal of Mathematical Physics, 55 (2014): 083516, 18 pages.
- Stability of viscous detonations for Majda's model (with Jeffrey Humpherys and Kevin Zumbrun), Physica D, 259 (2013): 63 - 80.
- The Gaussian semiclassical soliton ensemble and numerical methods for the focusing nonlinear Schrödinger equation (with Long Lee and Irena Vankova), Physica D, 241 (2012): 1767 - 1781.
- Spectral stability of ideal-gas shock layers (with Jeffrey Humpherys and Kevin Zumbrun), Archive for Rational Mechanics and Analysis, 194 (2009): 1029 - 1079.
- The N-soliton of the focusing nonlinear Schrödinger equation for N large (with Peter D. Miller), Communications on Pure and Applied Mathematics, 60 (2007): 951 - 1026.
- Equivalence of low-frequency stability conditions for multidimensional detonations in three models of combustion (with H. Kristian Jenssen and Mark Williams), Indiana University Mathematics Journal, 54 (2005): 1 - 64.
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.