Logic Colloquium: The Connes Embedding Problem and Model Theory

Colloquium | November 1 | 4-5 p.m. | 60 Evans Hall

 Isaac Goldbring, UC Irvine

 Department of Mathematics

The Connes Embedding Problem is the following problem in von Neumann algebras:  does every tracial von Neumann algebra embed into an ultrapower of a particular von Neumann algebra, the so-called hyperfinite $II_1$ factor $R$.  After the work of many mathematicians, this problem has been shown to have equivalent reformulations in C*-algebras, operator systems, quantum information theory, free probability, and geometric group theory, to name a few.

In this talk, I will discuss the many model-theoretic reformulations of this problem, including connections with existentially closed von Neumann algebras and computability of theories.  Some of the work presented in this talk is joint with Bradd Hart and Thomas Sinclair.  All relevant terminology from operator algebras will be defined.