Relative Calabi-Yau structures and moduli of objects

This talk is a report on joint work in progress with Chris
Brav. We introduce the concept of a Calabi-Yau functor between
smooth differential graded categories. Such a structure on the zero
functor $0 \rightarrow B$ recovers Ginzburg's notion of a Calabi-Yau category.
Various features of the resulting theory will be discussed, focussing
on the relationship with shifted symplectic and Lagrangian structures
when passing to moduli of objects.