“Remarks on definable Galois correspondence”

In this talk I will explain (review) why, working in a ω-stable theory, an (indirect) Galois correspondence always exists between definable subgroups of the definable group of automorphisms of a ”strongly normal type” and certain intermediate definably closed sets. The main point here is that our definition of strongly normal type does not require any ”closedness” condition on the fixed set of parameters. This subsumes several recent results around differential Galois theory.