Mathematical Institute, University of Oxford
Organizers: Minhyong Kim (Oxford), Ulrike Tillmann (Oxford), Bruno Vallette (Nice)
Grothendieck-Teichmüller theory goes back to Grothendieck's celebrated Esquisse d'un programme. In 1991, Drinfeld formally introduced two Grothendieck-Teichmüller 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 quasi-Hopf algebra). Introduced in algebraic topology 40 years ago, the notion of operad has enjoyed a renaissance in the 90's under the work of Kontsevich in deformation theory. Two proofs of the deformation quantization of Poisson manifolds, one by himself as well as one by Tamarkin, led Kontsevich to conjecture an action of a Grothendieck-Teichmüller group on such deformation quantizations, thereby drawing a precise relationship between the two themes.
More than 10 years after those major results, the underlying theories have now been well understood and we can expect new important discoveries. Recently, some results have been proved at the intersection of Grothendieck-Teichmüller groups, deformation theory, operads and multiple zeta values. These fields of research clearly overlap and lie at the forefront of current research in algebra, algebraic and differential geometry, number theory, topology and mathematical physics.
The Clay Mathematics Institute will hold a two-day workshop on 'Higher Structures in Topology and Number Theory' at the Mathematical Institute of the University of Oxford on 15 and 16 April 2013. The event is a satellite of the 'Grothendieck-Teichmüller Groups, Deformations and Operads' programme taking place at the Isaac Newton Institute in Cambridge between January and April 2013.