Knots and their Invariants

Abstract: This short course of 5 lectures will be a basic introduction to the study of knots and their invariants. After discussing the necessary knot theory basics, topics will be chosen from

1) Torus and satellite knots; braids and their connection to knots

2) Quantum mechanics, the Kauffman bracket, and polynomial invariants; Vassiliev invariants

3) Knot complements and three manifolds; Seifert surfaces and the genus of a knot; hyperbolic geometry, Mostow-Prasad rigidity, and applications to knot complements; software designed to compute hyperbolic invariants of knots.