Anti-de-Sitter solutions play an important role in the gauge-theory/gravity correspondence, and understanding their properties has provided important insights into the dual field theories. We consider ADS solutions which are highly supersymmetric, in the sense that they preserve more than 16 supersymmetries, and show how how modified versions of the homogeneity theorems of Figureoa-O'Farrill, combined with aspects of the global properties of the geometries, can be used to classify these solutions.

Spinorial geometry techniques provide new ways to analyze supersymmetric solutions of supergravity theories in a systematic fashion. I will describe how one can apply these methods to classify solutions of type IIB supergravity which preserve large amounts of supersymmetry. In particular, this provides a proof that solutions preserving exactly 31/32 of the supersymmetry do not exist, which resolves a long-standing open question.

The recent discovery of supersymmetric black ring solutions has important implications for black hole uniqueness and other aspects of black hole physics in higher dimensions. The construction of these solutions is investigated, and a generalization of the single ring solution to a system of concentric (multi-charge) rings is presented. The entropy of some of these solutions is particularly interesting.