Syllabus
1. Basic definitions and Examples
2. Gelfand-Naimark and continuous functional calculus
3. Positive elements, positivity and partial order
4. Hereditary C*-subalgebras
5. Functionals and representations
6. GNS construction
7. Representations
8. Completely positive maps
9. Tensor products
10. Inductive limits and AF algebras
11. Group C*-algebras
12. Crossed products
13. Groupoids
14. Groupoid C*-algebras
15. Twisted groupoid C*-algebras and Cartan subalgebras Some suggested self-study topics:
1. Cantor minimal systems
2. graph C*-algebras
3. classification AF algebras
4. Compact quantum groups
5. Cuntz algebras
Annotation
An introduction to the main concepts in C*-algebra theory, with the aim at preparing students to understand elements of contemporary research in the field. In particular, later parts of the course will focus on constructions from topological groupoids, a highly active area of research.