Mathematics Colloquia and Seminars

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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 begin by explaining this story for the well-studied case of toric varieties. Specializing to open toric manifolds, we will use intuition from the mirror side to define a symplectic invariant -- a completion of symplectic cohomology -- that captures local information. We will state a closed-string mirror theorem for an especially nice class of subdomains and make a mirror conjecture.