## Geometric Extremization for Supersymmetric $AdS_3$ and $AdS_2$ Solutions

We consider supersymmetric $AdS_3\times Y_7$ solutions of type IIB supergravity dual to N=(0,2) SCFTs in d=2, as well as $AdS_2\times Y_9$ solutions of D=11 supergravity dual to N=2 supersymmetric quantum mechanics, some of which arise as the near horizon limit of supersymmetric, charged black hole solutions in $AdS_4$. The geometry underlying these solutions was first identified in 2005-2007. Around that time infinite classes of explicit supergravity solutions were also found but, surprisingly, there was little progress in identifying the dual SCFTs.