John Rawnsley (University of Warwick)
Symplectic connections -- torsion free connections preserving a symplectic form on a manifold -- are the symplectic analogue of the Levi-Civita connection on a Riemannian manifold. Unlike the latter case, they are not unique and so are less closely linked to the geometry. Nevertheless they have played a role in Fedosov's construction of star products in deformation quantization, and in some constructions in mechanics. This talk will review existence and uniqueness as well as look at some curvature properties.