As an undergrad I had an interest in the theoretical underpinnings of physical laws. Topics that I spent a good deal of time playing around with, and found particularly interesting are:
- Coordinate (Lorentz) transformations, invariances, equivalences and the non-classical notions of special relativity
- The quantum measurement problem (or non-problem?), operators and state evolutions in Hilbert space, quantum information theory.
- Markov chains, collective dynamics, emergent properties and symmetry breaking in statistical mechanics.
It was a pleasant surprise to find that much of the techniques used to analyze neural networks are rooted in statistical mechanics and dynamical systems theory.
My physics senior research project investigated large-scale simulations of the many-body problem. Specifically, we performed computational analysis of the stability of planetary orbits to look for intermediate-range deviations from Newtonian gravitation as a result of the frequency shifts of free-falling oscillators. The initial simulations were set up in software, but we moved to a FPGA based simulation for hardware acceleration. I plan to continue this project in whatever free time (what's that?) I'll find in grad school.
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