Breakthroughs of which I am most proud:
1. Armstrong, E. Colonel Mustard in the Aviary with the Candlestick: a limit cycle attractor transitions to a stable focus via supercritical Andronov-Hopf bifurcation. https://arxiv.org/abs/1803.11559, 2018 April 1; PDF
2. Armstrong, E. A Neural Networks Approach to Predicting How Things Might Have Turned Out Had I Mustered the Nerve to Ask Barry Cottonfield to the Junior Prom Back in 1997. https://arxiv.org/abs/1703.10449, 2017 April 1; PDF
And here are suggested qualifying exam questions for physics graduate students at UC San Diego, which I wrote while studying for my own.