An introduction to $C^*$-algebras and $K$-theory II
This course extends the introductory study of $C^*$-algebras and $K$-theory introduced last semester, with a focused emphasis on classification of $C^*$-algebras using K-theoretic data. The interplay between functors $K_0$ and $K_1$ will be explored. Computational examples will be provided throughout the course, together with applications relevant to the classification of $C^*$-algebras.
Lecturer
Date
17th February ~ 18th May, 2025
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Monday,Thursday | 14:20 - 16:05 | A3-1-301 | ZOOM 06 | 537 192 5549 | BIMSA |
Prerequisite
Undergraduate Functional Analysis, General Topology, Algebra, An introduction to $C^*$-algebras and $K$-theory
Syllabus
1. Review of fundamental concepts of $C^*$-algebras and $K$-groups
2. The index map
3. The higher $K$-functors
4. Bott periodicity
5. The six-term exact sequence
6. Related topics (tensor product, etc.) in theory of $C^*$-algebras
7. Other topics in $K$-theory and classification
2. The index map
3. The higher $K$-functors
4. Bott periodicity
5. The six-term exact sequence
6. Related topics (tensor product, etc.) in theory of $C^*$-algebras
7. Other topics in $K$-theory and classification
Reference
1. Gerard Murphy, $C^*$-algebras and operator theory, Academic Press, Inc., Boston, MA, 1990. MR1074574 (91m:46084)
2. Mikael Rørdam, Flemming Larsen, and Niels Laustsen, An introduction to K-theory for $C^*$-algebras, London Mathematical Society Student Texts, vol. 49, Cambridge University Press, Cambridge, 2000. MR1783408 (2001g:46001)
3. Karen Strung, An introduction to $C^*$-algebras and the classification program, Advanced Course in Mathematics, Birkhaüser, CRM, Barcelona, 2021. MR 4225279
4. Ronald Douglas, Banach algebra techniques in operator theory. Second edition. Graduate Texts in Mathematics, 179. Springer-Verlag, New York, 1998. MR1634900 (99c:47001)
5. John Conway, A course in operator theory. Graduate Studies in Mathematics, 21. American Mathematical Society, Providence, RI, 2000. MR1721402 (2001d:47001)
6. Bruce Blackadar, $K$-theory for operator algebras. Second edition. Mathematical Sciences Research Institute Publications, 5. Cambridge University Press, Cambridge, 1998. MR1656031 (99g:46104)
2. Mikael Rørdam, Flemming Larsen, and Niels Laustsen, An introduction to K-theory for $C^*$-algebras, London Mathematical Society Student Texts, vol. 49, Cambridge University Press, Cambridge, 2000. MR1783408 (2001g:46001)
3. Karen Strung, An introduction to $C^*$-algebras and the classification program, Advanced Course in Mathematics, Birkhaüser, CRM, Barcelona, 2021. MR 4225279
4. Ronald Douglas, Banach algebra techniques in operator theory. Second edition. Graduate Texts in Mathematics, 179. Springer-Verlag, New York, 1998. MR1634900 (99c:47001)
5. John Conway, A course in operator theory. Graduate Studies in Mathematics, 21. American Mathematical Society, Providence, RI, 2000. MR1721402 (2001d:47001)
6. Bruce Blackadar, $K$-theory for operator algebras. Second edition. Mathematical Sciences Research Institute Publications, 5. Cambridge University Press, Cambridge, 1998. MR1656031 (99g:46104)
Audience
Advanced Undergraduate
, Graduate
, Postdoc
, Researcher
Video Public
No
Notes Public
No
Language
English
Lecturer Intro
He graduated from the University of Tokyo in 2018, and then became an associate research fellow at University of Tokyo. After finishing his postdocteral position at East China Normal University in 2022, He joined BIMSA as an assistant professor in 2023. He's recent research interests lie in classification theory of C*-algebras, C*-dynamical systems and topological dynamical systems.