Albert Much, PhD

• Lecturer: Albert Much (ITP, Leipzig university)

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• Lecture: Ringvorlesung - Noncommutative Geometry and Deformation Quantization

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• Date & Time: Friday (July 17, July 24, July 31), 13.00-14.30

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• Room: Videobroadcast (Link)

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• Audience: IMPRS students (mandatory in their first year), Phd students, postdocs

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• Abstract: 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.

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• Part 1 (pdf, video), Part 2 (pdf, video), Part 3 (pdf, video 1, 2), Part 4 (pdf 1, 2, video 1, 2)