Multiple polylogarithms, and Zagier's Conjecture revisited

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• Herbert Gangl (Durham University)
• Wednesday 11 May 2022, 16:00-17:00
• Seminar Room 2, Newton Institute.

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KAH2 - K-theory, algebraic cycles and motivic homotopy theory

Instigated by work of Borel and Bloch, Zagier formulated his Polylogarithm Conjecture in the late eighties and proved it for weight 2. After a flurry of activity and advances at the time, notably by Goncharov who provided not only a proof for weight 3 but set out a vast program with a plethora of conjectural statements for attacking it, progress seemed to be stalled for a number of years. More recently, a solution to one of Goncharov’s central conjectures in weight 4 has been found. Moreover, by adopting a new point of view, work by Goncharov and Rudenko gave a proof of the original conjecture in weight 4.   In this talk I intend to give a rough idea of the developments from the early days on, avoiding most of the technical bits, and, time permitting, also hint at a number of recent results for higher weight with new formulas for Grassmannian and Aomoto polylogarithms in terms of iterated integrals (joint with S.Charlton and D.Radchenko).

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

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