Deformation Quantization and Formality Theorem
摘要：In this talk, we give an introduction to the theory of deformation quantization (also called star product) of Poisson manifolds. Especially we introduce Kontsevich's formality theorem, which states that the differential graded Lie algebras (DGLA) of multi-vector fields and multi-differential operators on a smooth manifold are quasi-isomorphic homotopy Lie algebras. We give some examples of Poisson manifolds and star products and introduce the Schouten-Nijenhuis bracket, which makes the space of multi-vector fileds into a graded Lie algebra. Then we give a brief introduction to the deformation theory of associative algebras via DGLA. Combined, these theories provide material which allows us to understand and appreciate Kontsevich's formality theorem.