Foam evaluation and Khovanov–Rozansky link homologies (joint work with Emmanuel Wagner)

Foams are surfaces with singularities and can be thought of as cobordisms between graphs. I will present a formula which associate with any foam a symmetric polynomial in $N$ variables. Then I will explain that this formula extends to a trivalent TQFT which categorifies the $\mathfrak{sl}_N$-MOY calculus. This can be used to define the equivariant $\mathfrak{sl}_N$ link homology.
Surprisingly, the same formula can be used categorify the $\mathfrak(N)$ link invariant associated with symmetric powers of the standard representation of $U_q(\mathfrak{sl}_N})$ (aka the colored Jones polynomial in the case $N=2$).