Let X be a compact symplectic manifold, and D a normal crossings symplectic divisor in X. We give a criterion under which the quantum cohomology of X is the cohomology of a natural deformation of the symplectic cochain complex of X \ D. The criterion can be thought of in terms of the Kodaira dimension of X (which should be non-positive), and the log Kodaira dimension of X \ D (which should be non-negative). The crucial tool is Varolgunes’ relative symplectic cohomology.
This is joint work with Strom Borman and Umut Varolgunes.
This video is part of the Institute for Advanced Study‘s Symplectic geometry seminar.
