Georgia Institute of Technology College of Sciences

Vassiliev knot invariants, or finite-type invariants, are a broad class of knot invariants resulting from extending usual invariants to knots with transverse double points. We will show that the Conway and Jones polynomials are fully described by Vassiliev invariants. We will discuss the fundamental theorem of Vassiliev invariants, relating them to the algebra of chord diagrams and weight systems. Time permitting, we will also discuss the Kontsevich integral, the universal Vassiliev invariant.