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The Aomoto polylogarithm via iterated integrals

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KA2W03 - Mathematical physics: algebraic cycles, strings and amplitudes

Aomoto generalised the classical polylogarithm by assigning to a pair of n-simplices in |P^n a (multi-valued) integral. The Aomoto dilogarithm, in weight n=2, was written in terms of the classical dilogarithm by Beilinson, Goncharov, Schechtman and Varchenko, and subsequently Goncharov also expressed the Aomoto trilogarithm in terms of its classical version.We give the first—surprisingly short—expression of the Aomoto polylogarithm, in arbitrary weight, in terms of iterated integrals. The latter have been related to algebraic cycles (Bloch-Kriz in depth 1, G.-Goncharov-Levin for generic cycles in any depth). (Joint with Steven Charlton and Danylo Radchenko.)

This talk is part of the Isaac Newton Institute Seminar Series series.

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