AbstractIn 1991 Eliashberg-Floer-McDuff proved that compact symplectic manifolds of dimension at least 6 that bound the standard contact sphere symplectically are diffeomorphic to the ball provided there are no symplectic 2-spheres. This fundamental result raised the question whether the boundary of a symplectic manifold determines the interior. In my talk I will explain how holomorphic curves can be used to answer this open question. For example, symplectically aspherical fillings of simply-connected, subcritically fillable contact manifolds are unique up to diffeomorphism.

Note: This seminar is aimed at a general audience of mathematicians