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Tuesday, October 13, 2015

**Abstract:** We will define Hopf-Galois extensions of ring spectra and give some examples from chromatic homotopy theory. We also describe a method of producing intermediate extensions from normal-sub-Hopf-algebras, similarly to the way one produces intermediate Galois extensions from normal subgroups of the Galois group. We finally describe ongoing work to use this structure to streamline the proof of the Nilpotence Theorem of Devinatz, Hopkins and Smith.