Toward a Galois theory of the integers over the sphere spectrum

Abstract

Recent work [1,2,7,18,44] in higher algebra allows the reinterpretation of a classical description [8,11,31,32] of the Eilenberg-MacLane spectrum HZ as a Thom spectrum, in terms of a kind of derived Galois theory. This essentially expository talk summarizes some of this work, and suggests an interpretation in terms of configuration spaces and monoidal functors on them, with some analogies to a topological field theory.