GrothendieckTeichmüller Groups, Deformation and Operads Cambridge University

 Education
GrothendieckTeichmüller theory goes back to A. Grothendieck's celebrated Esquisse d'un programme. In 1991, V. Drinfel'd formally introduced two GrothendieckTeichmüller groups, the former one related to the absolute Galois group and the latter one related to the deformation theory of a certain algebraic structure (braided quasiHopf algebra). Introduced in algebraic topology 40 years ago, the notion of operad has enjoyed a renaissance in the 90's under the work of M. Kontsevich in deformation theory. Two proofs of the deformation quantization of Poisson manifolds, one by himself as well as one by D. Tamarkin, led M. Kontsevich to conjecture an action of a GrothendieckTeichmüller group on such deformation quantizations, thereby drawing a precise relationship between the two themes.
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