Title: Quantization is Deformation

Speaker: Daniel Sternheimer

Institution: Institut de Mathématiques de Bourgogne, Dijon, France

Abstract

We start with a short exposition of developments in physics and mathematics that preceded, formed the basis for, or accompanied, the birth of deformation quantization in the seventies. We indicate how the latter is at least a viable alternative, autonomous and conceptually more satisfactory, to conventional quantum mechanics and ultimately to the theory of quantized fields. We review related questions. These include existence and classification, explicit formulas, covariance and star representations of Lie groups, the Hopf avatar of deformation quantization a.k.a. quantum groups, the ``duality," in the sense of a (so far, not enough developed) noncommutative version of the Gelfand isomorphism, between quantization of algebras and symmetries, and quantization of space.