Finite nuclear dimension for C*-algebras is an important regularity property which appears in the classification theory for C*-algebras, and so it becomes an important question to understand how to compute (or at least bound) nuclear dimension. Graph C*-algebras provide a rich but tractable class of examples to look at, and they have been useful in helping to develop techniques to compute nuclear dimension. Even so, much is still not yet understood about the nuclear dimension for graph C*-algebras: it is conjectured to be at most 1 regardless of the underlying graph, but this has only been proven for certain classes of graphs. In this talk, I will discuss ongoing joint work with Jianchao Wu, where we are able to show that there is at least a uniform finite bound for the nuclear dimension of arbitrary graph C*-algebras.
