Projects

Fourier Transform on $\mathbb{R}$

A proof-first set of notes that builds the Fourier transform from definition to inversion with clean derivations.

Quantitative Modulus Control of Annuli on $\mathbb{C}$

An exploration using numerical methods derived from exploring holomorphic transformations.

Glauber Dynamics Simulator

A simulation of Glauber dynamics for spin systems, showcasing phase transitions and critical phenomena.

Coupling a Geometric State Space on $C_4$

Derivation of a coupling argument for a geometric state space on the cycle graph $C_4$.

ASML Stock Pitch

A long thesis on ASML as the sole EUV lithography supplier, tying AI-driven semiconductor capex to multi-year visibility.

Conway Mutation and the Jones Polynomial

We construct bracket vectors for 2-tangles, then show Conway mutations in the context of the Jones polynomial.

Exploring Euler-Product Surrogates

A detailed derivation of a statement concerning the implication of prime-indexed random walks.