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 (syllabus)
  • Math 1337 : Calculus I, Fall 2020 (syllabus)

Brown University

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

Pedagogical training

Code

AUTOdocker

AUTO is a publicly available software package used for continuation and bifurcation problems in ordinary differential equations and dynamical systems. It was written in 1980 and has been continually updated and maintained since then. Docker is a platform that delivers OS-level virtualization via packages called containers. Running AUTO in a Docker container allows the software to be run in a standard environment which is consistent across all platforms. You no longer have to install AUTO on your system. Interfacing with AUTO can be done using both the command line and Jupyter notebooks. This package contains Jupyter notebooks for most of the AUTO demos. These notebooks interface with AUTO to run the relevant demos, as well as plot the resulting solutions and bifurcation diagrams.