In this talk, I will first give a brief introduction to the Landau-Ginzburg -- Conformal Field Theory (LG-CFT) correspondence, a prediction from physics. This prediction links aspects of Landau-Ginzburg models, described by matrix factorisations for a polynomial known as the potential, with Conformal Field Theories, described by for example vertex operator algebras. While both sides of the correspondence have good mathematical descriptions, it is an open problem to give a mathematical formulation of the correspondence.
After this introduction, I will discuss the only known realisation of this correspondence, for the potential $x^d$. For even $d$ this is a recent result, and I will give a sketch of the proof which uses the tools of module tensor categories
I will not assume prior knowledge of matrix factorisations, CFTs, or module tensor categories. This talk is based on joint work with Ana Ros Camacho.