Calabi-Yau structures and finite loop spaces

We review the theory of Calabi-Yau structures on proper DG categories and their relation to 2d topological field theory, then construct a Calabi-Yau structure on the category of local systems on the classifying space of a connected finite loop space. Much of the talk will review various constructions with local systems that are less familiar than they deserve. This is joint work with N. Rozenblyum.