On the birational Grothendieck-Teichmueller Group GT

The Grothendieck-Teichmueller Group GT was introduced by Ihara and Drinfel'd, inspired by Grothendieck's "dessins d'enfants," in an effort to give a non-tautological description of the absolute Galois group G_Q of the rational numbers. It is still a widely open question whether the canonical embeddings of G_Q into GT -e.g. using Deligne's "tangential base points"- are isomorphisms, or even whether G_Q and GT are isomorphic as abstract profinite groups. In this talk I will define birational variants of GT, and answer in positive the above questions for the birational variants of GT under discussion. The technical tools originate from techniques developed (by several experts) to tackle Bogomolov's birational anabelian program.