College of Liberal Arts & Sciences

# Operator Theory Seminar

**Abstract:**

A special class of inner amenable groups are those which are stable in the sense of Jones and Schmidt. For stable groups, there always exists an action that gives rise to a cross product von Neumann algebra which is a McDuff II$_1$ factor, i.e. $M \cong M \otimes \mathcal{R},$ where $\mathcal{R}$ is the hyperfinite II$_1$ factor. Following the work of Bashwinger and Zaremsky, we show that a certain class of groups arising from the Thompson-Like group construction of Skipper and Zaremsky are stable groups, providing new examples of McDuff von Neumann algebras. Time permitting, I will discuss other properties of the group von Neumann algebra of Thompson's group $V.$ This is joint work with Rolando de Santiago and Krishnendu Khan.

**UICapture link to recordings:**