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Grothendieck-Teichmüller Theory and Multiple Zeta Values

8th April 2013 to 12th April 2013

Organisers: Herbert Gangl (Durham), John Jones (Warwick), Pierre Lochak (Paris VI) and Bruno Vallette (Nice)

Scientific Advisors: Giovanni Felder (ETH Zürich), and Alexander Goncharov (Yale)

Workshop Theme

Grothendieck-Teichmüller theory was day dreamt (as 'Galois-Teichmüller theory') by Grothendieck in his Longue Marche à travers la théorie de Galois and Esquisse d'un programme. It was then 'pioneered' by Y. Ihara and V.G. Drinfel'd whose famous 1989 paper fits especially well into the overall theme of this programme since it introduces a novel form of 'universal' deformation theory. The same year P. Deligne explained in his equally famous paper on the thrice punctured projective line the connection between Grothendieck-Teichmüller theory, Multiple Zeta Values and mixed Tate motives.

It should be noted however that in the mind of Grothendieck himself, 'Galois-Teichmüller' theory was not supposed to be exclusively or even primarily motivic, extending in particular to the consideration of moduli stacks of curves of any genus.

The workshop will also be an opportunity for discussing this more topological side of the theory, along with the elliptic (genus 1) theory for Polylogarithms and their special values which currently features the 'frontier' case of the motivic side of the theory.

This overly compressed historical introduction can help make sense of the following incomplete list of the themes which this workshop will touch upon:

  • Associator and double shuffle relations.
  • Mixed Tate motives and motivic fundamental groups.
  • Mixed Hodge structures and fundamental groups.
  • Polylogarithms and variations of mixed Hodge structures.
  • Grothendieck-Teichmüller theory in a motivic framework.
  • Functional equations of polylogarithms and K-theory.
  • Elliptic polylogarithms and their special values.
  • Grothendieck-Teichmüller theory: higher genus.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons