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.
- Evans function computation for the stability of travelling waves, (with Blake Barker, Jeffrey Humpherys, and Joshua Lytle), Preprint, 25 pages, 2017. (Accepted for publication in Philosophical Transactions of the Royal Society A)
- Euler vs. Lagrange: The role of coordinates in practical Evans-functions computations, (with Blake Barker, Jeffrey Humpherys, and Kevin Zumbrun), arXiv:1707.01938.
- Balanced flux formulations for multidimensional Evans function computations for viscous shocks (with Blake Barker, Jeffrey Humpherys, and Kevin Zumbrun), arXiv:1703.02099. (Accepted for publication in Quarterly of Applied Mathematics)
- Analysis and development of compact finite difference schemes with optimized numerical dispersion relations (with Yi-Hung Kuo and Long Lee), arXiv:1409.3535.
- Multidimensional stability of large-amplitude Navier-Stokes shocks (with Jeffrey Humpherys and Kevin Zumbrun), Archive for Rational Mechanics and Analysis, 226 (2017): 923 - 973.
- 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.