I'm a grad student in the math department at UC Berkeley. I like computational complexity, cryptography, geometry and topology, categories, and doing explicit computations about mathematical objects on the computer, among many other things. Here are some things I think are beautiful and cool:

• Pseudorandomness
• Large scale geometry
• Variations on the notion of proof (interactive proofs, PCPs, zero knowledge proofs, arguments, lambda terms)
• Categorification
• Erdős's proof that there are infinitely many primes

• Is there a simple proof that every faithful rep of \(S_n\) has dimension at least \(n - 1\)?
• Can we use the rep theory of \(S_n\) to prove circuit lower bounds?
• When can we assume uniform inclusions of complexity classes?
• How much are vector bundles like complexity classes?

Recent blog posts

• Purely mathematical results from complexity theoretic assumptions: Systolic geometry edition.
• Indistinguishability amplification
• Quadratic proof-complexity lower bounds from large scale geometry