Title: Residually Dominated Groups
Abstract: This talk is about the model theory of henselian valued fields whose residue field has characteristic zero. A well-known fact about the pure theory of these fields is that their first-order properties are controlled by the residue field and the value group, which are comparatively simpler structures. In this talk, we investigate types and definable groups that are controlled entirely by the residue field sort. These notions are analogous to stably dominated types and groups, which play a central role in the model theory of algebraically closed valued fields. I will begin with an overview of the literature and then present the main results from our joint work with Paul Wang.