Topology Seminar: Motivic homotopical Galois extensions

(Joint work with Agnès Beaudry, Magdalena Kedziorek, Mona Merling, and Vesna Stojanoska)  I will sketch a formal framework for homotopical Galois extensions, motivated by the case of commutative ring spectra developed by Rognes,  within which we can prove invariance of Galois extensions under extension of coefficients and  the forward part of a Galois correspondence.  I will explain why both motivic spaces and motivic spectra fit into this framework, then provide explicit examples of motivic homotopical Galois extensions, some of which have no classical analogue.