Supersymmetric AdS/CFT and black holes

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The AdS/CFT correspondence is a duality between string/M-theory in Anti-de-Sitter spacetime and conformal field theories. It continues to illuminate both our understanding of quantum field theory and of quantum gravity. Furthermore, it is associated with interesting geometric structures. The broad goals are to further our understanding of AdS/CFT in a supersymmetric context and explore the new geometric structures that arise. A goal will be to obtain new insights into deriving the entropy of classes of supersymmetric AdS black holes. A rich framework which will be explored, is provided by classes of supersymmetric AdS3 solutions of type IIB supergravity, dual to d=2 supersymmetric conformal field theories as well as supersymmetric AdS2 solutions of D=11 supergravity, which arise as the near horizon limit of supersymmetric black hole solutions. In both case there is an odd dimensional compact internal manifold which supports a GK geometry.The solutions can arise from D3 branes and M2 branes wrapping compact two dimensional surfaces and an interesting sub-class consists of two-dimensional orbifolds known as spindles. These topics will be investigated in order to obtain new insights into the AdS correspondence.