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SUMMARY:Multiple polylogarithms\, and Zagier's Conjecture revisited - Herb
 ert Gangl (Durham University)
DTSTART:20220511T150000Z
DTEND:20220511T160000Z
UID:TALK174224@talks.cam.ac.uk
DESCRIPTION: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 wit
 h 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.\n&nbsp\;\nIn this talk I intend to
  give a rough idea of the developments from the early days on\, avoiding m
 ost 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.Charlt
 on and D.Radchenko).
LOCATION:Seminar Room 2\, Newton Institute
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