Geometric aspects of the AdS/CFT correspondence / Michael T. Anderson -- Some aspects of the AdS/CFT correspondence / Jan de Boer, Liat Maoz, Asad Naqvi -- The ambient obstruction tensor and Q-curvature / C. Robin Graham, Kengo Hirachi -- AdS/CFT correspondence and geometry / Ioannis Papadimitriou, Kostas Skenderis -- Mass formulae for asymptotically hyperbolic manifolds / Marc Herzlich -- Reconstructing Minkowski space-time / Sergey N. Solodukhin -- Non-trivial, static, geodesically complete space-times with a negative cosmological constant II. n ≥ 5 / Michael T. Anderson, Piotr T. Chruściel, Erwann Delay -- The conformal boundary of anti-de Sitter space-times / Charles Frances -- Supersymmetric AdS backgrounds in string and M-theory / Jerome P. Gauntlett, Dario Martelli, James Sparks, Daniel Waldram.

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Since its discovery in 1997 by Maldacena, AdS/CFT correspondence has become one of the prime subjects of interest in string theory, as well as one of the main meeting points between theoretical physics and mathematics. On the physical side it provides a duality between a theory of quantum gravity and a field theory. The mathematical counterpart is the relation between Einstein metrics and their conformal boundaries. The correspondence has been intensively studied, and a lot of progress emerged from the confrontation of viewpoints between mathematics and physics. Written by leading experts and directed at research mathematicians and theoretical physicists as well as graduate students, this volume gives an overview of this important area both in theoretical physics and in mathematics. It contains survey articles giving a broad overview of the subject and of the main questions, as well as more specialized articles providing new insight both on the Riemannian side and on the Lorentzian side of the theory.