I will review known results about the degeneration of the Hodge-de Rham spectral sequence for categories of matrix factorizations. In particular I will discuss a condition that has appeared in unexpected ways in work of Arinkin, Hablicsek and myself, and independently in work of Teleman.

I will conclude by explaining how new ideas from topological Hochschild homology are supposed to help in proving the degeneration directly, but don’t (yet).