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Grothendieck-Teichmüller theory

Presented by: 
P Lochak Institut de Mathématiques de Jussieu
Tuesday 8th January 2013 - 14:00 to 15:00
INI Seminar Room 2
In this talk I am planning to review both the first inputs and some of the main sources and currents of Grothendieck-Teichmueller theory. I will start by quickly recalling the existence of an action of the arithmetic Galois group on (various versions of) the fundamental group of an algebraic variety (resp. scheme, stack) in general, then single out (as Grothendieck first did) the moduli stacks of curves, which feature the defining objects of GT theory. I will then give some indications about the contents of four `pionneering' papers, by A.Grothendieck, V.Drinfel'd, Y.Ihara and P.Deligne respectively. This will lead in particular to underlining some crucial differences in goals and approaches for the various (at least two) versions of the theory, which of course are still in the making.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons