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Ross Parker

Ph.D. Student in Applied Mathematics

Brown University

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.

In my spare time, I enjoy Scottish country dancing, Sacred Harp singing, playing piano and violin, origami, and ultralight backpacking.

Research

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.

Double pulses in KdV5 (left) and DNLS (center). Corresponding eigenvalue pattern on right.

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.

Teaching

Brown Univerity

Instructor

  • APMA 1360 : Applied Dynamical Systems (Spring 2020)
  • Intensive review for incoming graduate students (Summer 2019)
  • APMA 1650 : Statistical Inference I (Summer 2016)

Teaching assitant

  • APMA 0350 : Applied ordinary differential equations (Spring 2016)
  • APMA 1650 : Statistical Inference I (Fall 2015)

Pedagogical training

Recent & Upcoming Talks

Spectral stability of periodic multi-pulses in the 5th order KdV equation

Spectral stability of multi-pulses via the Krein matrix

Stability of double pulse solutions to the 5th order KdV equation