Lecture 1: 2D TFT with defects and matrix factorisations

Abstract: there is a rich theory surrounding the fusion of defects in Landau-Ginzburg models. I will review the basic theory of matrix factorisations and their associated categories, and introduce the operation of tensor product of matrix factorisations which is interpreted as fusion of defects. I will then go through numerous examples in the mathematics and physics literature, including permutation type defects (motivated by conformal field theory) and stabilisations of bimodules (coming from knot homology).

(see www.therisingsea.org for lecture slides)

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