Writing
Arguments, notes, and working models.
Long-form work across algebraic geometry, cryptography, quantitative finance, and the systems around them.
07 entries
How Geometric Torsion at Sub-Planck Lengths Prevents the Existence of Special Classes of Residual D-Branes
A walk from a polynomial drawing a circle to the proof that the Kuznetsov component of a generic Enriques surface admits no Serre-invariant Bridgeland stability condition. Serre invariance negates numerical classes, while an explicit projected point is fixed — an impossible sign contradiction.Supersymmetry and the Extra Dimensions That Refuse to Stay Hidden
The Higgs boson sits 17 orders of magnitude below where quantum mechanics says it should. Supersymmetry was designed to fix that — and even as the LHC leaves it empirically pressured, the algebraic structure it revealed keeps generating mathematics.Supersingular Isogeny Diffie-Hellman: A Beautiful Idea That Almost Worked
SIDH was the most mathematically elegant post-quantum key exchange candidate — compact keys, deep algebraic structure — until a 1997 genus-2 paper destroyed it in under an hour on decade-old hardware.Algebraic Geometry for the Computationally Inclined
Where algebraic geometry ships in 2026: elliptic curves and BLS12-381 in cryptography, Reed–Solomon and AG codes in storage and deep-space comms, polynomial-system solvers inside SLAM and parallel robotics. A long-form tour for engineers who write code but never took the graduate course.Notes on Options Pricing
Options pricing is a parabolic PDE in disguise. From Black–Scholes-as-heat-equation to rough volatility, deep BSDE solvers, and signature methods: what the 3D surfaces on quant Twitter actually are, and where the math behind them lives.Notes on Hierarchical Risk Parity
Why those wavy 3D return landscapes on quant Twitter are Hierarchical Risk Parity in disguise — and what the math underneath does for your portfolio.