Arithmetic Study Group: Topological methods in Grothendieck-Teichmueller theory
27 October 2009 16:15 in CM219
I will try to cover part of what could called geometric (as contrasted with `motivic') Grothendieck-Teichmueller theory, which started around twenty years ago, partly following (with delay) Grothendieck's `Sketch of a program'. Among the topics that will be touched upon are: the algebraic fundamental group, arithmetic Galois action on the fundamental group, the case of the projective line with three points and `dessins d'enfants', moduli stacks of curves and the Grothendieck Teichmueller group. I will explain in particular how one can topologically understand (and prove a version of) the `two level principle', which lies at the root of the very existence of the Grothendieck-Teichmueller group and its ubiquity.