This research investigates polynomial invariants of knots and links in three-dimensional space. The main invariant under investigation is a two-variable generalization of the Jones polynomial that is due to the principal investigator. This invariant and related viewpoints are being used to prove conjectures about alternating knots, make new models for the Jones polynomial, examine embeddings of graphs (with possible applications in chemistry and molecular biology) and to draw connections between knot theory and statistical physics.
