An introduction to C*-algebras and K-theory
This course offers an introductory exploration of the fundamental principles of $C^*$-algebras and $K$-theory with emphasis on classification of $C^*$-algebras using K-theoretic data. The first part of this course delves into the essential aspects of $C^$-algebras, which are helpful to introducing $K$-theory. These include the Gelfand representation, Gelfand-Naimark-Segal construction, and Gelfand-Naimark representation. The second part is devoted to the introduction of $K_0$-groups for $C^*$-algebras, covering their basic properties and exploring Elliott's classification of AF-algebras. Finally, the course proceeds to introduce $K_1$-groups.
Lecturer
Date
18th September ~ 15th December, 2023
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Monday,Friday | 09:50 - 11:25 | A3-1a-205 | ZOOM 09 | 230 432 7880 | BIMSA |
Prerequisite
Undergraduate Functional Analysis, General Topology, Algebra
Syllabus
Fundamentals of the theory of $C^*$-algebras
Projections and unitaries
$K_0$-groups for unital $C^*$-algebras
$K_0$-groups for general $C^*$-algebras
Order structure of $K_0$-groups
Inductive limit $C^*$-algebras
Classification of AF-algebras
$K_1$-groups for $C^*$-algebras
Projections and unitaries
$K_0$-groups for unital $C^*$-algebras
$K_0$-groups for general $C^*$-algebras
Order structure of $K_0$-groups
Inductive limit $C^*$-algebras
Classification of AF-algebras
$K_1$-groups for $C^*$-algebras
Reference
Gerard Murphy, $C^*$-algebras and operator theory, Academic Press, Inc., Boston, MA, 1990. MR1074574 (91m:46084)
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)
Karen Strung, An introduction to $C^*$-algebras and the classification program, Advanced Course in Mathematics, Birkhaüser, CRM, Barcelona, 2021. MR 4225279
Ronald Douglas, Banach algebra techniques in operator theory. Second edition. Graduate Texts in Mathematics, 179. Springer-Verlag, New York, 1998. MR1634900 (99c:47001)
John Conway, A course in operator theory. Graduate Studies in Mathematics, 21. American Mathematical Society, Providence, RI, 2000. MR1721402 (2001d:47001)
Bruce Blackadar, $K$-theory for operator algebras. Second edition. Mathematical Sciences Research Institute Publications, 5. Cambridge University Press, Cambridge, 1998. MR1656031 (99g:46104)
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)
Karen Strung, An introduction to $C^*$-algebras and the classification program, Advanced Course in Mathematics, Birkhaüser, CRM, Barcelona, 2021. MR 4225279
Ronald Douglas, Banach algebra techniques in operator theory. Second edition. Graduate Texts in Mathematics, 179. Springer-Verlag, New York, 1998. MR1634900 (99c:47001)
John Conway, A course in operator theory. Graduate Studies in Mathematics, 21. American Mathematical Society, Providence, RI, 2000. MR1721402 (2001d:47001)
Bruce Blackadar, $K$-theory for operator algebras. Second edition. Mathematical Sciences Research Institute Publications, 5. Cambridge University Press, Cambridge, 1998. MR1656031 (99g:46104)
Audience
Undergraduate
, Graduate
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.