Residually finite dimensional C*-algebras arising in dynamical contexts

A C*-algebra is said to be residually finite-dimensional (RFD) when it has `sufficiently many' finite-dimensional representations. The RFD property is an important, and still somewhat mysterious notion, with subtle connections to residual finiteness properties of groups. In this talk I will present certain characterisations of the RFD property for C*-algebras of amenable étale groupoids and for C*-algebraic crossed products by amenable actions of discrete groups, extending (and inspired by) earlier results of Bekka, Exel, and Loring. I will also explain the role of the amenability assumption and describe several consequences of our main theorems. Finally, I will discuss some examples, notably these related to semidirect products of groups.