Abstract: 

Let T be an extension of the theory of fields of characteristic zero, and suppose that model-theoretic and field-theoretic algebraic closure coincide in every model of T (i.e. T is algebraically bounded). Fornasiero and Terzo proved that if one expands models of T by a derivation (or by several derivations, either commuting or non‑commuting), the resulting theory has a model completion. Since then, a number of authors have investigated how much the model theory of this model completion is controlled by that of T. Recent work includes the transfer of combinatorial tameness properties, the behavior of independence relations, bounds on ranks, and descriptions of definable sets, groups, and fields. In this talk, I will survey several of these developments, along with some connections to the differentially large fields studied by León Sánchez and Tressl.

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