Random Researchy Things

I wrote a bit about my current research interests in my “About” section. But mathematics research is messy, and a great deal of time is dedicated to working through dense/arcane/okseriouslywhatareyousaying texts in an attempt to make sense of it all. I wanted a place to dump my own musings, and while I fully expect the stuff I post here to be replete with errors, naive intuition, and general confusion, I still wanted to put it somewhere. A small optimistic part of me hopes that it’s useful to someone who is curious about mathematics.

So take everything here with a grain of salt, and I hope it’s useful to somebody! Please let me know if you did find some use out of it.

Quantum Spin Systems

AKLT model ground states (Summer 2020)

Majumdar-Ghosh model ground states (Winter 2021)

Spectral Theory

Convergence of powers of matrices with simple largest eigenvector to the Perron Projection (Summer 2020)

  • This isn’t my proof, but the result is beautiful and one of my favorites–as a use case, it guarantees exponential convergence of a starting distribution on a graph to the simple largest eigenvector’s distribution for “nice” Markov chains in Google’s PageRank algorithm!
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