NMAK13030U Approximation Properties for Operator Algebras and Groups (Approx)
MSc Programme in Statistics
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This course aims at providing a comprehensive treatment of a number of approximation properties for countable groups and their corresponding counterparts for von Neumann algebras and C*-algebras. This will include the following topics: amenable groups, nuclear C*-algebras, injective von Neumann algebras, exactness for C*-algebras and groups, the completely contractive and completely bounded approximation properties (CCAP and CBAP, respectively) and the Haagerup property (property H). If time permits, Kazhdan's property T for groups and von Neumann algebras will also be discussed.
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.
Nathanial P. Brown, Narutaka Ozawa: C*-algebras and finite dimensional approximations, Graduate Texts in Mathematics Vol. 88, Amer. Math. Society, Providence, Rhode-Island, 2008, and research papers.
- Category
- Hours
- Lectures
- 36
- Preparation
- 152
- Theory exercises
- 18
- Total
- 206
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- Credit
- 7,5 ECTS
- Type of assessment
- Continuous assessmentEach student will give a 2x45 min presentation of material (not covered in lectures) relevant to the topic of the course, coming either from a research paper or from the textbook itself.
- Marking scale
- passed/not passed
- Censorship form
- No external censorship
One internal examiner.
- Re-exam
- Oral, 30 minutes with preparation time with all aids, several internal examiners.
Criteria for exam assesment
The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome.
Course information
- Language
- English
- Course code
- NMAK13030U
- Credit
- 7,5 ECTS
- Level
- Full Degree Master
- Duration
- 1 block
- Placement
- Block 2
- Schedule
- A (Tues 8-12 + Thurs 8-17)
- Course capacity
- No limit.
- Continuing and further education
- Study board
- Study Board of Mathematics and Computer Science
Contracting department
- Department of Mathematical Sciences
Course responsibles
- Magdalena Elena Musat (5-6f77756376426f63766a306d7730666d)