Abstracts for Seminar "Multicurve invariants in Khovanov homology"

We introduce the Bar-Natan category, defined via cobordisms modulo local relations, giving a diagrammatic formulation of Khovanov homology. We outline its extension to tangles and the resulting functorial invariant.

This talk presents a purely topological model for wrapped Fukaya categories of surfaces, avoiding symplectic geometry and analytical techniques. The construction is based on combinatorial data of arcs and trajectories on surfaces, yielding a triangulated category that models the wrapped Fukaya category in a topological way. As an application, we obtain a homological mirror symmetry correspondence with gentle algebras arising from the same surface data.