Daniel J. Lynch

Daniel J. Lynch

he/him/his

Postdoc and teaching assistant at Northwestern University. My interests include limbed locomotion for robotic exploration in complex environments, nonlinear dynamics, geometric mechanics and control, granular rheology, fluid mechanics, and gait rehabilitation and prosthetics.

Volunteer Teacher

Splash at Northwestern (Education Outreach), Northwestern University

In 2022 and 2023, I volunteered as a teacher for Splash at Northwestern, an education outreach program dedicated to providing unique and fun learning opportunities to high school students in the greater Chicago area, especially students coming from underrepresented backgrounds. Each year, I designed and taught a course that applied various topics in mathematics to aspects of real life: ecology (2022) and music (2023).

  • Rabbits and Foxes, Butterflies and Tornadoes, and Chaos (2022)
  • The Mathematics of Modern Musical Harmony (2023)

Rabbits and Foxes, Butterflies and Tornadoes, and Chaos (April 2, 2022)

In this one-day course, I introduced several concepts related to nonlinear dynamics and chaos theory, and I illustrated these concepts using a progression of examples from ecology:

  • single-species exponential growth
  • single-species logistic growth
  • two-species predator-prey dynamics (Lotka-Volterra equations - limit cycle oscillations in predator and prey populations)
  • three-species population dynamics example 1: omnivory
  • three-species population dynamics example 2: scavenging

Both three-species examples (omnivory and scavenging) can undergo a cascade of period-doubling bifurcations leading to chaos.

You can watch a YouTube video I created based on this course.

The Mathematics of Modern Musical Harmony (May 27, 2023)

Was legendary jazz saxophonist John Coltrane also a mathematician? When people talk about the mathematical beauty of music, Bach is among the most-mentioned classical composers, but Coltrane pushed musical harmony miles beyond anything Bach and his contemporaries did, and the methods he used to get there have a surprisingly elegant mathematical foundation: graph theory, which has a wide array of applications, including social network analysis and robot navigation.

Before introducing graph theory to the class as a method for formalizing chord changes, I developed the Circle of Fifths from (as much as possible) first principles and made some informal connections to topology.

I ran four sessions of this course, and received positive feedback from students in each session who enjoyed our shared experience digging into the overlap between math and music.