The goal of this workshop is to initiate a dialogue between mathematicians and physicists working to understand mathematical aspects of the $AdS$ / $CFT$ correspondence. Some concrete goals include the construction of simple examples of $AdS_3$ / $CFT_2$ correspondence, the development of the mathematical theory of topological twists of $AdS$ / $CFT$ and the construction of new $N$ = 1 $CFT$s arising from quiver gauge theories dual to non-toric Calabi-Yau cones.