Examples and constructions: We will consider some simple constructions of low-dimensional symplectic manifolds; how they look from the point of view of holomorphic curve theory; and what the use of Lagrangian submanifolds can add to that picture.

Flux and related invariants: Starting with the classical notion of flux, we will consider new invariants of symplectic manifolds associated to odd cohomology classes. These are related to the derived Picard groups of homotopical algebra.

Hidden symmetries: Certain classes of symplectic manifolds show non-geometric symmetries. These can be used to produce refined intersection numbers and monodromy maps. If time permits, we will explain the relation with mirror symmetry.