Papers:

2.) A crucial ingredient in the theory of Categorical Enumerative Invariants is a splitting of the non-commutative Hodge filtration (related to a trivialization of the circle action on Hochschild chains of a Calabi-Yau category), from which a formality morphism is constructed. In my second paper I explain how to construct a formality morphism in the open-closed theory of Categorical Enumerative Invariants, again depending on a splitting. Physically, an instance of such a open-closed theory is  BCOV theory coupled to holomorphic Chern-Simons.

1.) In my first paper I explain how various versions of the Loday-Quillen-Tsygan map, respectively a generalization that applies to (cyclic) A-infinity categories, various graph complexes, additionally equiped with shifted Poisson or BV-algebra structure, and Kontsevich's cocycle construction are linked together. 

This is related to what is called open (topological) String Field Theory (SFT). Its cousin is closed SFT, as described by Sen-Zwiebach, Costello, Căldăraru-Tu, which led to the definition of Categorical Enumerative Invariants; its field theoretic avatar should be BCOV theory, as developed by Costello-Li.