about
background.
I am a mathematician by training.
research interests.
My early research work focused on the behavior of solutions of nonlinear partial differential equations, especially in scenarios where those solutions represent important physical phenomena. Most of those projects featured an interplay of elements from some combination of rigorous real, complex, and functional analysis; numerical computation; dynamical systems; and/or modern asymptotic methods.
More recently, my interests have broadened to include data-driven modeling and machine learning for healthcare applications. In the healthcare domain, I am especially interested in the interaction between data and model, and the wide variety and utility of “real” health data.
other stuff about me.
I grew up in Fort Wayne, Indiana (the one-time magnet wire capital of the world). Outside of mathematics, I love alpine skiing (my happy place is an undisclosed location somewhere near the Bar-UE lift at Steamboat), attempting to solve the New York Times crossword puzzle, drinking (and occasionally trying to make) good coffee. My wife and I live in Minneapolis, MN with a retriever mix named Penny.
oldies but goodies.
Some papers of which I am especially fond for one reason or another…
- Long Lee, Gregory Lyng, & Irena Vankova, The Gaussian semiclassical soliton ensemble and numerical methods for the focusing nonlinear Schrödinger equation. Physica D, 241 (2012): 1767–1781.
- Jeffrey Humpherys, Gregory Lyng, & Kevin Zumbrun, Spectral stability of ideal-gas shock layers. Archive for Rational Mechanics and Analysis, 194 (2009): 1029–1079.
- Gregory Lyng & Peter D. Miller, The N-soliton of the focusing nonlinear Schrödinger equation for N large. Communications on Pure and Applied Mathematics, 60 (2007): 951–1026.
- H. Kristian Jenssen, Gregory Lyng, & Mark Williams, Equivalence of low-frequency stability conditions for multidimensional detonations in three models of combustion. Indiana University Mathematics Journal, 54 (2005): 1–64.