I am an RTG postdoctoral fellow in the Department of Mathematics at Southern Methodist University. I received my Ph.D. in applied mathematics from Brown University, where I worked with Björn Sandstede on the stability of nonlinear waves. In particular, I studied the existence and stability of multi-pulse solutions in continuous and discrete Hamiltonian systems. I also collaborate with Alejandro Aceves, Todd Kapitula and Panos Kevrekidis.
Although I have been fascinated by mathematics as long as I can remember, it took me until my mid 30s to embrace my inner math nerd. Beforehand, I worked many different jobs, including bicycle repairperson, computer network technician, church organist, math and science tutor, emergency room technician, and internal medicine intern.
In my spare time, I enjoy Scottish country dancing, Sacred Harp singing, playing piano and violin, origami, and ultralight backpacking.
Ph.D. in applied mathematics, 2020
Brown University
Solitary waves are localized disturbances in a medium that maintain their shape as they propagate at a constant velocity. I study the existence and stability of multi-pulse solitary waves in Hamiltonian systems such as the fifth-order Korteweg-de Vries equation (KdV5) and the discrete nonlinear Schrodinger equation (DNLS). Multi-pulses are disturbances which resemble multiple, well separated copies of a single solitary wave.
I am interested in how the geometry of a multi-pulse solution determines its spectral stability. My research statement summarizes the work I have done on multi-pulses.