computing Khovanov invariants for links and tangles

Khovanov Cobordism Calculator is a Python module to calculate cobordism maps induced on Khovanov homology.

A Python package for interactive visualizations of Legendre knots and Contact Structures

GEOKNOT: a geometrically biased algorithm to sample spaces of knotted objects.

Code and results from my thesis project: Jupyter notebooks aligned with Chapters 3-6. Read the thesis chapters for context before exploring.

To derive the mysterious mass hierarchy of quarks (e.g., Why is Top quark so heavy?) by mapping particle generations to Prime Knots of increasing crossing number.

A Python package for working with Seifert fibered spaces.

My master's thesis in low-dimensional topology

GAP programs for tabulating generalized Legendrian racks (also called GL-racks or bi-Legendrian racks) up to order 11. Data for all GL-racks up to order 8.

A reproducible, audit-first Python workbench for the invariants of smooth 4-dimensional topology — native Khovanov, Lee, Rasmussen s, and knot Floer homology for knots, links, and braids, validated against established tools.

Two papers and pure-Python code for the knot Atiyah–Floer program of the P(−2,3,q) pretzel family: the rank of instanton knot homology I♮, a computed deficiency law, and the first nonzero bounding cochains in pillowcase Floer theory.

A geometry-first physics research program: the complete, adversarially-audited record of the bet that physics is the geometry of a 3-manifold (time emergent as modular flow) — including the honest negative result and the standalone Heegaard Floer d-invariant math that stands on its own.

Scripts, certificates, and papers reducing a homeomorphism question for Lidman–Piccirillo 4-manifolds to the exotic S²×S² problem, plus a certificate-complete computation of π₁ via coset enumeration and Knuth–Bendix completion.