Georgia Institute of Technology College of Sciences

We will start by defining the Jones polynomial of a knot and talking about some of its classical applications to knot theory. We will then define a fancier version ("categorification") of the Jones polynomial, called Khovanov homology and mention some of its applications. We will conclude by talking about a further refinement, a Khovanov homotopy type, sketch some of the ideas behind its construction, and mention some applications. (This last part is joint work with Sucharit Sarkar.) At least the first half of the talk should be accessible to non-topologists.