Spinorial geometry, horizons and superconformal symmetry in six dimensions

The spinorial geometry method of solving Killing spinor equations is reviewed as it applies to 6-dimensional (1,0) supergravity. In particular, it is explained how the method is used to identify both the fractions of supersymmetry preserved by and the geometry of all supersymmetric backgrounds. Then two applications are described to systems that exhibit superconformal symmetry. The first is the proof that some 6-dimensional black hole horizons are locally isometric to $AdS_3\times \Sigma^3$, where $\Sigma^3$ is diffeomeorphic to $S^3$. The second one is a description of all supersymmetric solutions of 6-dimensional (1,0) superconformal theories and in particular of their brane solitons.