String Theory Journal Club

Khovanov homology is a powerful invariant introduced by Mikhail Khovanov in 2000. This link invariant, which categorifies Jones polynomial, was nicely reinterpreted by Viro in a purely combinatorial way in terms of Kauffman states. In this introductory talk we will review the main properties of Khovanov homology, starting from this combinatorial construction, and presenting some explicit examples. Moreover, in the second part of the talk I will present our geometric realization of extreme Khovanov homology in terms of a simplicial complex constructed from the independence graph associated to a link diagram.