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

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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