Quantum cohomology as a deformation of symplectic cohomology

Quantum cohomology as a deformation of symplectic cohomology

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Nick Sheridan, University of Edinburgh

Zoom link:  :  https://umontreal.zoom.us/j/94366166514?pwd=OHBWcGluUmJwMFJyd2IwS1ROZ0FJdz09   

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.