Algebraic combinatorics seminar - David Jackson

A Quantum Invariant of Knots

Abstract:

This will be an informal talk about knot invariants which will not presuppose any background in knot theory. The theory is rich in combinatorial constructions combined with specific algebras. Thus the area also serves as a rich context for studying the combinatorial and enumerative properties of these algebras. Such algebras include Hopf algebras  and Lie algebras, and their combinatorialisation (for example, through Penrose's diagrammatic tensor calculus). My aim is to reach the Reshetikhin-Turaev Theorem for constructing invariants, and then to show how the Jones polynomial, the invariant of the title, may be deduced from it.