Writing

• Complex cobordism and formal group law Stanford undergraduate honours thesis, which gave a detailed proof to a complex cobordism push-forward formula that Quillen sketched in private notes. I thought about extending this to include source manifolds that arise in Gromov-Witten theory.
• A note on compressing BN254 curve pairing values My evaluation on implementing a 3x compression method for pairing values from the BN254 curve and performance evaluation, where I explore subtleties that arise from optimized multiplication for elliptic curves and their performance implications. The documentation is here: https://jolt.a16zcrypto.com/how/optimizations/compression.html.
• A result about the subgroup of trace zero in the BN254 curve A proof for a result about the BN254 curve which is widely used in cryptography and zk-SNARK system implementations.
• Fast field trace computation from tower of field extensions Optimize lattice cryptography, making a certain trace map 32x faster, from Galois Theory 101.
• Trace pairing (lattice crypto) Conceptualize a packing inner product via standard trace perfect pairing on number fields, extending results to non-2-power degree cyclotomic extensions in lattice cryptography.

Talks

• p-Ordinary Cohomology Groups for SL(2) over Number Fields (after Hida), Hida theory seminar, Columbia University, 2026

Notes

• Space of self-dual connections of instanton number 1 I learnt Floer theory from Ciprian Manolescu when I was a Stanford undergrad. This document is my write-up on the space of t’Hooft connections from reading courses taken in 2022 my junior year, where I learnt instanton Floer homology, Heegaard Floer, Seiberg-Witten, and Donaldson’s construction of exotic R4. Back then, I was interested in various flavors of Floer homology, which involve using delicate analytic tools to construct invariants that turn out to have rich combinatorial and algebraic properties in low-dimensional topology and symplectic geometry. I still find this subject fascinating, especially the connections to homotopy theory through Morse theory. I also did summer research on Khovanov homology and bordered Heegaard Floer. I strongly recommend The Wild World of 4-Manifolds. If you’re a complexity theorist, you might be interested to learn that word problems for braid groups are “solved” by Khovanov homology, and knot polynomials compute path integrals.