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# Operator Algebra and Noncommutative Geometry Seminar Series

## September 28, 2017 @ 3:30 pm - 4:30 pm

##### Title

Type semigroups for ample groupoids, and applications

##### Speaker

Prof Aidan Sims (UOW)

##### Abstract

A great deal of recent progress on the stably finite/purely infinite dichotomy for simple C*-algebras has been driven by Rordam and Sierakowski’s introduction of the type semigroup of an action of a group on a zero-dimensional space. I will discuss recent joint work with Tim Rainone that extends this notion to ample Hausdorff groupoids, so that the type semigroup of a transformation groupoid coincides with Rordam and Sierakowski’s type semigroup for the action. I’ll outline how the type semigroup is defined, how it can be extended to non-compact unit spaces, and how it can be computed for some key classes of examples.