Specifically, consider $X$ an infinite compact metric space, $\mathcal{V}$ a locally trivial vector bundle over $X$ and $\alpha : X \to X$ a homeomorphism (often assumed minimal). We can construct a $\text{C}^*$-correspondence $\mathcal{E}$ over $C(X)$ from the module of sections of $\mathcal{V}$, where we use the homeomorphism $\alpha$ to twist the left multiplication. As we shall see, many tractable and interesting $\text{C}^*$-correspondences over $C(X)$ do in fact arise in this manner.

In this talk, I will discuss some of the structural properties and classification of the resulting Cuntz-Pimsner algebra $\mathcal{O}(\mathcal{E})$. Under the additional assumption that $\mathcal{V}$ is a line bundle the Cuntz-Pimsner algebra is a generalized crossed product, suggesting additional means of investigation. For Cuntz-Pimsner algebras arising from line bundles we can construct orbit-breaking subalgebras of $\mathcal{O}(\mathcal{E})$ and show that they are centrally large in the sense of Phillips.

This is based on joint work with Maria Stella Adamo, Dawn Archey, Marzieh Forough, Ja A Jeong, Karen Strung and Maria Grazia Viola.

There are multiple natural senses in which two operator algebras may have "the same" C*-covers, and we will discuss how these different senses remember different information about the operator algebras involved. Along the way, we will see how to construct a simple operator algebra that is not similar to a C*-algebra. This is joint work with Dr. Christopher Ramsey.