Due to the rather broad spectrum of topics within the IMPRS, the curriculum consists of a core curriculum to be attended by all students and a variety of more specialized lectures and courses. The heart of our teaching program certainly is the Ringvorlesung. Each semester the Ringvorlesung focuses on one field and is usually delivered by scientific members of the IMPRS who introduce different approaches and visions within this field.
- Lecturer: Albert Much (ITP, Leipzig university)
- Date & Time: Friday (July 17, July 24, July 31, August 7), 13.00-14.30
- Room: Videobroadcast
- How to participate: To participate please send an email to the Scientific Coordinator of the IMPRS.
- Audience: IMPRS students (mandatory in their first year), Phd students, postdocs
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.