Matrix factorizations and the Landau-Ginzburg/conformal field theory correspondence

The Landau-Ginzburg/conformal field theory correspondence is a physics result from the late 80's and early 90's which in particular relates categories of representations of vertex operator algebras and categories of matrix factorizations. Up to date, there is no precise mathematical conjecture for this result. We present some recent progress on this topic, based on joint work with Nils Carqueville, Alexei Davydov and Ingo Runkel.