Research

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Conway Mutation and the Jones Unknot Problem

A paper detailing that the Jones polynomial is invariant under Conway mutation, using bracket vector notation.

exposition topology tikz technical

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Coupling Bounds for Glauber Colorings

A clean comparison of classical/path coupling bounds for single site Glauber dynamics on $q$ colorings.

reproducibility MCMC python C++

publication ↗

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Notes for Fourier Transform on $\mathbb{R}$

A clean layout for a detailed proof providing a step-by-step derivation of the inversion for the Fourier transform.

presentation latex

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Quantitatively Controlled Holomorphic Maps

A validated sequence of experimentations aimed at deriving a special annulus via holomorphic control.

analysis proof latex

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Random Euler-Product Surrogates

Developing a strong statement, and proving small-surrogate cases on i.i.d random $\zeta$.

expository notes

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Feature-Extraction Machine Learning

Developed, innovated, and implemented a new way to conduct first-round application holistic reviews.

demonstration innovation

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● status: current Research building Write-ups & proofs time --:-- LIVE