Noncommutative Geometry via Deformation Quantization
摘要：In this talk, we introduce a noncommutative version of the theory of Riemannian geometry via deformation quantization of Poisson structures. We will discuss noncommutative metrics, connections, curvatures and Bianchi identities and how they relate to classical ones. We also formulate noncommutative Einstein field equations. We will compute noncommutative curvatures of some explicit noncommutative surfaces.