From Landau-Ginzburg to Matrix factorisations and TQFT

Landau-Ginzburg models have been used in various areas of mathematical physics. For example, there is a close link between them and sigma models with Calabi-Yau targets, thus making them interesting for String theory. Without going into details on these motivations, I will present Landau-Ginzburg models as an interesting example of dealing with boundary terms by introducing additional fields on the boundary (while partially preserving supersymmetry). The resulting mathematical structure is matrix factorisation. These can be used to build TQFTs from Landau-Ginzburg models which gives a different perspective on physically known results.