The 3rd MSJ-SI

The Mathematical Society of Japan, Seasonal Institute

Development of Galois-Teichmüller Theory
and Anabelian Geometry

October 25 Monday, 14:30--15:20
P. Lochak (CNRS)
Grothendieck-Teichmüller theory from a topological viewpoint
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.