Closed-string mirror symmetry predicts a matching of dynamical information (on the symplectic side) with a ring of functions (on the mirror side). Mysteriously, while the mirror invariants can be defined locally, the symplectic invariants arise as global phenomena. We will use intuition from the mirror side to define a symplectic invariant -- a completion of symplectic cohomology -- that captures local information.

Specializing to toric Fano examples, we will state a closed-string mirror theorem for an especially nice class of subdomains. We will end with a mirror conjecture for moving beyond the Fano case.