Homotopical Galois extensions of E_\infty algebras

Rognes generalised the classical notion of Galois extensions from algebra to homotopy theory of ring spectra. In recent work with Beaudry, Hess, Merling and Stojanoska we discussed a general formal framework in which the notion of (homotopical) Galois extensions can be studied and we applied that work to the motivic homotopy theory. 

In this talk I will recall the general framework for homotopical Galois extensions and present an ongoing work with Hess on homotopical Galois theory for E_\infty - algebras.