and Anabelian Geometry

October 25 Monday, 14:30--15:20 | |

P. Lochak
(CNRS)
Grothendieck-Teichmüller theory from a topological viewpoint
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I will survey part of what could called geometric (as contrasted with 'motivic') Grothendieck-Teichmüller theory, which started around twenty years ago, partly following (with delay) Grothendieck's 'Sketch of a program'. 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-Teichmüller group and its ubiquity. Time permitting I will then delineate a program centered around completed versions of the so-called curve complexes which should help unify (and hopefully attack) certain conjectures on moduli stacks of curves and their fundamental groups. |