NSCPHD1254 Approximation Properties for Operator Algebras and Groups (Approx)

After completing the course, the students will have:

Knowledge of the material mentioned in the description of the content.

Skills to to read and understand research papers concerning topics discussed in lectures.

The following competences:

• Have a good overview and understanding of the various approximation properties for groups and their associated von Neumann algebras, respectively, group C*-algebras discussed in lectures. In particular, understand how these approximation properties for the group reflect into corresponding properties for the associated operator algebras.
• Master (at a satisfactory level) the fundamental results covered in the lectures, to the extent of understanding their proofs and be able to interconnect various results.
• Have a good understanding and be able to work with completely positive maps (respectively, completely bounded maps), which are the natural morphisms in the setting of the course.
• Handle complex results connecting various topics within the area of von Neumann algebras and C*-algebras, as well as approximation properties of discrete groups.