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Abstract: The word "generic" is often applied to a theory T* when it arises as a model companion of a base theory T. Generic theories exhibit lots of "random" behavior, so they are rarely stable or NIP, but they can sometimes be shown to be simple by characterizing a well-behaved notion of independence in T* (namely non-forking independence) in terms of independence in T. Recently, there has been increased interest in the property NSOP1, a generalization of simplicity, spurred by the work of Chernikov, Kaplan, and Ramsey, who showed that NSOP1 theories can also be characterized by the existence of a well-behaved notion of independence (namely Kim independence). In this talk, I will present a number of preservation results for simplicity and NSOP1 under generic constructions. In joint work with Nicholas Ramsey, generic expansion and generic Skolemization: add new symbols to the language, interpreted arbitrarily or as Skolem functions, and take the model companion. And in very recent results towards a joint project with Minh Chieu Tran and Erik Walsberg, interpolative fusion: given an L_1-theory T_1 and and L_2-theory T_2, which intersect in an L_0-theory T_0, take the model companion of the union of T_1 and T_2.