In these two talks, we shall first review non-commutative (NC) hodge theory of differential graded categories, such as Hochschild homology, cyclic homology, and NC hodge filtration. These notions can be packaged to form so-called semi-infinite hodge structures (SHS). We then discuss variations of SHS’s (VSHS), which is then used to introduce a categorical version of Saito’s primitive forms. Along the way, we shall work with the category of matrix factorizations as our primary example of the general theory.