Louis H Kauffman, Knots, Graphs and Groups, 29.04.23.

Knots, Graphs and Groups seminar at MIPT, Russia
Title: From Colorings to Virtual Links and Back
Speaker: Louis H Kauffman, UIC
Abstract: This talk continues the previous talk on "epsilon" but will be self contained. We review the formulation of graph colorings in terms of colored circuits (formations) and how it applies to a proof of the Penrose formula. We generalize the Penrose formula in two directions - one to obtain coloring counts for all cupid graphs - the other to make a perfect matching polynomial. The perfect matching polynomial is then mapped by a correspondence to virtual link theory to meet the bracket polynomial. This in our work with Baldridge and Rushmore creates a conduit between virtual graphs and virtual links that is under investigation. The talk will discuss this correspondence.