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Recent work in higher algebra allows the reinterpretation of a classicaldescription of the Eilenberg-MacLane spectrum $H\mathbb{Z}$ as a Thom spectrum,in terms of a kind of derived Galois theory. This essentially expository talksummarizes some of this work, and suggests an interpretation in terms ofconfiguration spaces and monoidal functors on them, with some analogies to atopological field theory.

Toward a Galois theory of the integers over the sphere spectrum