The project is a 3 stage Conference centered on very recent developments in mathematical theories of deformations inspired by their applications in various domains of theoretical physics. The main part of the first event (almost half) deals with deformation quantisation and its various avatars, including Kontsevich's formality and Connes' non-communitative geometry. The second event (half size, in number of participants), and about half of the third event, will be devoted to developments expected in these areas, with again active participation of both leaders and other experts. Indeed dramatic developments have occurred in the past year in that area, culminating last April with seminal papers by both leaders, in a special issue of Lett. Math. Phys. put on the web. The first deals with the role of operads and motives in deformation quantisation and goes far beyond the previous paper on quantisation of Poisson manifolds which is now extensively studied in seminars and conferences.
The papers by the second show the prominence of Hopf algebras in recent progress in Quantum Field Theory and the consistency of cyclic cohomology (on which non commutative geometry is based) with Hopf algebra theories (including quantum groups, another avatar of deformation quantisation). Another application of deformation theory is physics in anti De Sitter universe considered as a deformation of Minkowskian space-time, related symmetry group deformations, their representations, covariant field equations and field theories built on them. This includes singletons, conformal covariance and the much studied in the past years (in the framework of string theories) AdS/CFT correspondence. Progress in that domain will be presented in the first and third event, together with new developments in nonlinear covariant field equations and "plain" quantum physics needed for a comprehensive view, presented by leading experts.