Ross Parker

Ross Parker

RTG postdoctoral fellow

Southern Methodist University

Biography

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.

Interests

  • Dynamical systems
  • Nonlinear waves
  • Network theory

Education

  • Ph.D. in applied mathematics, 2020

    Brown University

Research

Stability of solitary waves

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.

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.

Teaching

Southern Methodist University

  • Math 3304 : Introduction to Linear Algebra (Spring 2021)
  • Math 1337 : Applied Dynamical Systems (Fall 2020)

Brown Univerity

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

Pedagogical training

Presentations

Instability bubbles for multi-pulse solutions to Hamiltonian systems on a periodic domain
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