# A survey of the model theory of tracial von Neumann algebras

## Isaac Goldbring

### University of Illinois Chicago

Von Neumann algebras are certain algebras of bounded operators on Hilbert spaces. In this talk we will survey some of the model theoretic results about (tracial) von Neumann algebras, focusing mainly on (in)stability, quantifier-complexity, and decidability. No prior knowledge of von Neumann algebras will be necessary. Some of the work presented is joint with Ilijas Farah, Bradd Hart, David Sherman, and Thomas Sinclair.

Professor Goldbring is an Assistant Professor in the Mathematics Department at the University of Illinois at Chicago, working in the field of mathematical logic, especially model theory. His specific research interests include: Pure and applied model theory, Nonstandard analysis, Model theory for metric structures, Lie theory, Geometric group theory and Operator algebras.