Albert Much: Ringvorlesung


In this "Ringvorlesung" we introduce basic concepts of noncommutative geometry and deformation quantization. We begin by introducing the metric aspect and generalizations of commutative concepts to the noncommutative realm, such as differential forms, know as the universal differential algebra. Further on, we will introduce spectral geometry to see applications of the framework.
Once these results are established we move on to deformation quantization. First we introduce the conceptual ideas and later we sketch the proof of the famous Kontsevich theorem, for which he obtained the Fields medal. Next, we introduce the more strict (i.e. non-formal) approach to deformation quantization known by the Rieffel Deformation. In the last part of this lecture series we show how noncommutative geometry and Deformation quantization are connected by the example of a simple quantum gravitational toy model.

Regular lectures: Summer semester 2020

03.08.2020, 02:30