The WueCampus course is now available. The first to register wins the COOKIE AWARD.

This Research in Groups aims at master students in the programs International Master in Mathematics, Mathematics, and Mathematical Physics. It may also be interesting for students in the master program Physics.

The course consists of essentially two components: first, a lecture where the basic notions of deformation quantization are explained. The preliminary program for the lecture component includes the following topics:

- Quantization for R
^{2n}and first star products - Symbol calculus for differential operators and quantization of cotangent bundles
- Star products on symplectic manifolds
- Fedosov construction of star products
- Fedosov construction on cotangent bundles

The second component will be a seminar by the students on more particular topics. We expect the participants to write a small proceeding-like summary of their seminar talks. The following topics are available:

- Integral formulas and Rieffel's approach
- Wick type star products and Fedosov construction on Kähler manifolds
- Fedosov construction for vector bundles, bimodule structures, Morita theory
- Characteristic classes of star products a la Gutt-Rawnsley
- Traces, existence and uniqueness
- Examples beyond cotangent bundles: complex projective space, the disk, the Gutt star product on the dual of a Lie algebra, Fedosov construction for duals of Lie algebroids
- Phase space reduction of star products, BRST/Koszul approach

Many of the topics can also be shared by two or more students. The precise content of the talks and the corresponding literature will be explained individually.

For this RiG you will need some background in differential geometry and perhaps geometric mechanics. In addition, some interest in the physical concepts related to the interplay of classical and quantum mechanics might be useful but not necessary.

If you are in doubt, please contact us directly and we will find a solution. We will explain the necessary things either in the lecture part or directly.

The following list of references will be discussed in the first meeting. More references will be given individually.

If there are collisions with other lectures or seminars, please contact me early: maybe one can still shift things around a bit.

- Lecture:
- Seminar: The seminar will take place at one or two days at the end of the semester. The precise date will be announced.

- On WueCampus there will be a homepage for this RiG. The WueCampus homepage will replace this site as soon as it is activated.

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