Title: Ribbon Hopf Algebras Viewed Topologically

Abstract: This is an expository talk on how the category of modules for a Ribbon Hopf Algebra can be used to define framed knot invariants and in some cases knot invariants. The talk will be based on the work of Reshetikhin and Turaev from the 1990s. We will first look at what a framed knot is and how invariants for framed knots can be defined. Then starting from just an algebra A and building up to a Ribbon Hopf Algebra, we will see how the category A-Mod can be viewed topologically using diagrams that will eventually represent framed knots. At the end, we will briefly see how the Jones Polynomial can be recovered from the Ribbon Hopf Algebra U_q(sl(2)).