Universal construction, foams and link homology

This talk is based on a joint work with Mikhail Khovanov. In this work we review the construction of sl(N) link homology theory coming from foams, which categorifies HOMFLY-PT link invariant and RT sl(N) quantum link invariants. This talk is elementary, the emphasis will be put on the theory of unoriented SL(3) foams, their evaluation and corresponding universal construction. This version of foam theory is related to 4-color theorem and Kronheimer-Mrowka 3-orbifold homology theory. If time permits, we will also talk about how oriented SL(3) foams categorify the Kuperberg invariant.