Witt algebra acts on Khovanov-Rozansky homology / Skein module of the Dehn filling of a small knot

by Alexis Guérin (Université Clermont-Auvergne), Edwin Kitaef (Université de Bourgogne)

Friday 13 Nov 2026, 11:00 → 13:00 Europe/Brussels

B/2nd floor-B.203 - Seminar room (Marc de Hemptinne (chemin du Cyclotron, 2, Louvain-la-Neuve))

11 a.m. : Alexis Guérin (Université Clermont-Auvergne) : Witt algebra acts on Khovanov-Rozansky homology.

Categorification of polynomial invariants has led to the construction of homological invariants such as Khovanov homology. Lie algebra actions on link homologies were first investigated by Gorsky, Oblomkov, and Rasmussen, who conjectured that certain homologies have graded dimensions given by characters of representations of affine Lie algebras. Such actions were first constructed on HOMFLY-PT homology, initially for the positive half of the Witt algebra, by Khovanov and Rozansky. Qi, Robert, Sussan, and Wagner later constructed an action of the Lie algebra $\mathfrak{sl}_2$ on Khovanov–Rozanisky homology and suggested that this action could extend to the positive half of the Witt algebra. In this talk, I will present joint work with Felix Roz in which we construct an action of the positive half of the Witt algebra on Khovanov–Rozansky homology and its colored version.

 

2 p.m : Edwin Kitaef (Université de Bourgogne) : Skein module of the Dehn filling of a small knot.

The skein module of a 3-manifold M describes the combinatorics of links in M, extending in a sense the notion of the Jones polynomial. Its definition is elementary, and yet it is very difficult to compute. After presenting the skein module and some results about it, we will sketch a theorem that allows one to compute the skein module of 3-manifolds obtained by surgery on a small knot (for instance a two-bridge knot).