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SUMMARY:Herbert Gangl (Durham University)
DTSTART:20250312T160000Z
DTEND:20250312T170000Z
DTSTAMP:20260418T063705Z
UID:LNTS/155
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LNTS/155/">M
 ultiple polylogarithms\, and Zagier's Conjecture revisited</a>\nby Herbert
  Gangl (Durham University) as part of London number theory seminar\n\nLect
 ure held in Room 505\, Department of Mathematics (25 Gordon St)\, Universi
 ty College London.\n\nAbstract\nDirichlet related the residue at $s=1$ of 
 the Dedekind zeta function of a number field $F$ (a slight generalisation 
 of the famous Riemann zeta function) to two important arithmetical notions
 : the size of the ideal class group and the `volume' of the unit group in 
 the number ring $\\mathcal{O}_F$ of $F$. Generalising this surprising conn
 ection\, the special values of the Dedekind zeta function of a number fiel
 d $F$ at integer argument $n$ should\, according to Zagier's Polylogarithm
  Conjecture\, be expressed via a determinant of $F$-values of the $n$-th p
 olylogarithm function. Goncharov laid out a vast program incorporating thi
 s conjecture using properties of multiple polylogarithms and the structure
  of a motivic Lie coalgebra.\nIn this impressionist talk I intend to give 
 a rough idea of the developments from the early days on\, avoiding most of
  the technical bits\, and also hint at a number of recent results for high
 er weight\,  some in joint work with\, or developed by\, S. Charlton\, D. 
 Radchenko as well as D. Rudenko and his collaborators.\n
LOCATION:https://researchseminars.org/talk/LNTS/155/
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