Title: K-theory
Speaker: Thomas Schick
Institution: University of Göttingen
Date & Time:
December 13, 2024, 9:00–10:00
December 14, 2024, 9:00–10:00
December 14, 2024, 10:10–11:10
December 15, 2024, 9:00–10:00
Location: Room 209, Zhengxin Building, Jilin University
We introduce the K-theory groups of a C∗-algebra and explain their basic properties. In essence, the group K₀(A) classifies finitely generated projective A-modules, while K₁(A) classifies automorphisms of trivial modules. These groups arise in numerous contexts and simultaneously provide insights into the structure of the algebra A. We will outline computational tools and present initial applications.
Plan:
Long exact sequence of an extension
Matrix and compact operator stability
Product structure
Bott periodicity
Sample calculations (Calkin index sequence)
An overview of the Elliott classification program
Thomas Schick is a Professor of Mathematics at the Mathematisches Institut of the University of Göttingen. His research areas include Topology and Geometry, Geometry and Analysis, K-Theory of C*-algebras, and index theory. He served as the Managing Editor of
Mathematische Annalen (until April 2022). Currently, he is the Head of the Scientific Advisory Board of the Mathematischen Forschungsinstituts Oberwolfach (MFO) and an editor for
Annales Mathématiques Blaise Pascal,
Journal of Homotopy and Related Structures, and
Bulletin of the Iranian Mathematical Society.
