Stuart White- Classification of Simple Amenable C-Algebras

Explore the classification of simple amenable C*-algebras in this 47-minute lecture by Stuart White for the International Mathematical Union. Delve into operator algebras, examining structure and classification through examples from group actions and inductive limits. Investigate the role of traces as non-commutative invariant measures and the Elliott programme. Analyze higher-dimensional examples, considering topological dimensions and non-commutative tensor units. Gain insights into the fundamental aspects of C*-algebra structure and classification, building upon concepts from von Neumann algebras and Connes' work.

Intro
OPERATOR ALGEBRAS AN EXAMPLE
STRUCTURE AND CLASSIFICATION CLASSIFICATION
EXAMPLES FROM GROUP ACTIONS
EXAMPLES: INDUCTIVE LIMITS
STRUCTURE AND CLASSIFICATION OF VNAS
ONE OF MANY INGREDIENTS IN CONNES WORK
INVARIANTS FOR C-ALGEBRAS CAN SEE THE MATRIX SIZE IN THE C-INDUCTIVE LIMITS
TRACES: NON COMMUTATIVE INVARIANT MEASURES
ELLIOTT PROGRAMME
HIGHER DIMENSIONAL EXAMPLES
TOPOLOGICAL DIMENSION?
NON-COMMUTATIVE TENSOR UNITS?
C-ALGEBRA: STRUCTURE AND CLASSIFICATION