Classification of Operator Algebras: Complexity, Rigidity, and Dynamics

The theory of operator algebras was born shortly after quantum mechanics revolutionized physics, nearly 100 years ago. John von Neumann wanted a proper mathematical framework for the physicists’ new theory, so he started studying what are now referred to as von Neumann algebras (i.e., W*-algebras). Shortly after that, Israel Gelfand and Mark Naimark began a systematic study of so-called C*-algebras. Thanks to the work of some of the giants of 20th century mathematics, operator algebra theory has reached broader and deeper than anyone could have predicted. The classification theory for several classes of operator algebras, notably that of classifying nuclear C*-algebras by K-theoretic invariants, has made giant strides forward in recent years.

The research program will concentrate on rigidity and classification in C*-algebras and its interfaces with other operator algebras, dynamics, discrete structures, and descriptive set theory. The objective is to further the understanding of these topics through not only the participation of C*-algebra specialists, but also specialists in the specified related areas.

The main themes for the program will be:

• Classification and dynamical systems.
• Classification and discrete structures.
• Classification and set theory.

Workshop Classification and discrete structures

Master Class Quasidiagonality and classification of C*-algebras

Workshop Classification and dynamical systems I: C*-algebras

Workshop Classification and set theory

Workshop Classification and dynamical systems II: Von Neumann Algebras