Noncommutative geometry and quantization

Abstract

We examine some recent developments in noncommutative geometry, including spin geometries on noncommutative tori and their quantization by the Shale-Stinespring procedure, as well as the emergence of Hopf algebras as a tool linking index theory and renormalization calculations

26 pages, standard Latex, needs XyPic fonts. Lectures delivered at the X Jorge Andre Swieca Summer School on Particles and Fields, Sao Paulo, 7-12 February 1999