PhD thesis defence seminar

Omar Leon Sanchez, Pure Mathematics, University of Waterloo

"Contributions to the model theory of partial differential fields"

In this thesis three topics on the model theory of partial differential fields are considered: the generalized Galois theory for partial differential fields, geometric axioms for the theory of partial differentially closed fields and the existence of the model companion of the theory of partial differential fields with an automorphism. The approach taken here to these subjects is to relativize the algebro geometric notions of prolongation, D-variety, and D-group to differential notions with respect to a fixed differential structure.