Dendriform di-algebra algorithms to compute using Loday's arithmetic on groves of planar binary trees

This paper presents an explanation of integrability in statistical physics, quantum groups, & knot theory. It discusses the 6 vertex model, its connection to Yang-Baxter equation, leading to YB algebras & quantum groups. Introduces the Jones polynomial's connections to Artin's braid group & tangles, and role in defining quantum invariants of knots.

The LaTeX files of my dissertation and two related papers.