Seth Wolbert (UIUC Math) Parallel Transport and Principal Bundles for Geometric Stacks Abstract: It has been known for about 60 years that parallel transport for principal $G$-bundles with equivariant connections is characterized by holonomy homomorphisms and that these maps can be used to reconstruct not only the associated connection, but also the relevant bundle. This relationship has been most recently restated as an equivalence of categories between bundles with connections over a fixed manifold and a category of objects known as transport functors. I will describe recent work, done with Eugene Lerman and Brian Collier, to prove this equivalence is natural; furthermore, I will describe how this naturality allows us to extend the above characterization of parallel transport to bundles over Lie groupoids and, more generally, geometric stacks.