University of Toronto's Symplectic Geometry Seminar

Abstract: Suppose that a Riemannian manifold is deformed into a noncommutative geometry. The existence of such a deformation implies compatibility conditions between the metric and the Poisson structure of the deformation. These conditions are expressed in terms of a "contravariant connection" and a novel higher curvature tensor. As far as time allows, I will describe how to use these conditions, and the technique of symplectic realizations, to classify noncommutative deformations of compact Riemannian manifolds.