Department of Mathematics - Master Calendar

An Introduction to Khovanov Homology - Jonathan Higgins

The Jones polynomial is a well-known link invariant, discovered by Vaughan Jones in the 80s. It is very handy in low-dimensional topology, as it admits an easy combinatorial method for computation. We begin by describing how to compute it via the Kaufmann state model and the cube of resolutions. We then proceed to construct a homology theory, known as Khovanov homology, whose graded Euler characteristic is the Jones polynomial and which gives a stronger invariant. This provides a glimpse into the vast world of topological quantum field theories (TQFTs) and categorification.