Nils Carqueville

Topological defects and Khovanov-Rozansky homology



Abstract

Topological defects in affine Landau-Ginzburg models are described by matrix factorisations. We motivate some of their properties such as defect fusion and action on bulk fields, which we then treat rigorously by proving that the defect category has a pivotal rigid monoidal structure that is compatible with the triangulated structure. Furthermore, having defect fusion under good control allows for a direct and explicit computation of Khovanov-Rozansky link invariants, and we shall present various examples. The two parts of my talk are based on joint work with Ingo Runkel and Daniel Murfet, respectively.