Groupoids give a very large class of examples of C*-algebras. For example, it is known that every classifiable C*-algebra arises as the reduced C*-algebra of some twisted groupoid.

In joint work with Matthew Kennedy, Se-Jin Kim, Xin Li, and Sven Raum, we fully characterize when the essential C*-algebra of an étale groupoid $\mathcal{G}$ with locally compact unit space has the ideal intersection property. This is done in terms of the dynamics of $\mathcal{G}$ on the space of subgroups of the isotropy groups of $\mathcal{G}$. The essential and reduced C*-algebras coincide in the case of Hausdorff groupoids, and the ideal intersection property is the same as simplicity in the case of minimal groupoids. This generalizes the case of the reduced crossed product $C(X) \rtimes_r G$ done by Kawabe, which in turn generalizes the case of the reduced C*-algebra $C^*_r(G)$ of a discrete group done by Breuillard, Kalantar, Kennedy, and Ozawa.

No prior knowledge of groupoids will be required for this talk.