We will start with an introduction to categorification and proceed with examples of categorification in knot and graph theory.

We will discuss the proof of the conjecture due to M. Khovanov relating the algebraic and topological categorification of the chromatic polynomial. More precisely, there exist a spectral sequence from chromatic graph homology over algebra A defined by L. Helme-Guizon and Y. Rong, and the homology of a graph configuration space introduced by M. Eastwood, S. Huggett. The details and further generalization will be provided in next week's talk by V. Baranovsky.