Abstract:

In 1930's Murray and von Neumann discovered natural ways to construct von Neumann algebras from group actions on probability measure spaces, and (unitary) group representations. This led to fruitful connections between the study of von Neumann algebras and other areas of mathematics, such as ergodic theory and dynamical systems. In this talk, I will describe this mutual symbiosis between von Neumann algebras and other areas of mathematics. I will also describe some recent rigidity phenomena in von Neumann algebras. 

This talk will be accessible to graduate students with measure theory background.

*The Math Colloquium will be available live via Zoom at https://uiowa.zoom.us/j/99206823329 and recordings of the sessions will be available at https://uicapture.hosted.panopto.com/Panopto/Pages/Sessions/List.aspx?folderID=b23b61cc-a48a-4de7-99fc-ae46015b8b6e usually within a couple hours of the colloquium finishing.