I am a sixth-year Ph.D. student in the Division of Applied Mathematics at Brown University. I work with Björn Sandstede on stability of nonlinear waves. Specifially, I study the existence and stability of multi-pulse solutions to Hamiltonian systems. I also collaborate with 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. Before I came to my senses, I worked many different jobs, including bicycle repairperson, computer network technician, church organist, SAT instructor, emergency room technician, and internal medicine intern.
My main research interest is solitary waves, which are localized disturbances in a medium that maintain their shape as they propagate at a constant velocity. In particular, 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. For future work, I am interested in combining my biomedical and mathematical backgrounds. In particular, I am interested in applications of dynamical systems to neuroscience.