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Francis Brown : Periods, Galois theory and particle physics: Galois theory and transcendence

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Classical Galois theory replaces the study of algebraic numbers with group theory. This idea is extremely powerful, and led to the proof of the insolubility of the general quintic equation. A deep idea, originating in the work of Grothendieck, is that Galois theory should extend to the theory of periods. I will describe a cheap way to set up such a theory and illustrate it in the case of multiple zeta values. It gives rise to a symmetry group which respects the algebraic identities satisfied by these numbers and explains their underlying structure.

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