Seminars: Louis-Hadrien Robert, Foam evaluation and Khovanov--Rozansky link homologies (joint work with Emmanuel Wagner)

SEMINARS


Knots and Representation Theory April 1, 2019 18:30, Moscow

Foam evaluation and Khovanov–Rozansky link homologies (joint work with Emmanuel Wagner) Louis-Hadrien Robert Université de Genève
Abstract: 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 $N=2$). Language: English