## Special Colloquium

Robert Lipshitz

Columbia University

An introduction to Khovanov homology and homotopy

**Abstract:**Two of the most heavily-studied knot invariants are the Jones polynomial and a refinement of it called Khovanov homology. In the first part of the talk we define these invariants and state some of their topological applications. In the second part we will sketch a construction of a topological space whose ordinary homology is Khovanov homology, and give some potential applications of this refined invariant; this construction is joint work with Sucharit Sarkar.

Friday January 13, 2012 at 3:00 PM in SEO 636