  Placing D3-branes at conical Calabi-Yau threefold singularities produces many
AdS$_5$/CFT$_4$ duals. Recent progress in differential geometry has produced a
technique (called K-stability) to recognize which singularities admit conical
Calabi-Yau metrics. On the other hand, the algebraic technique of
non-commutative crepant resolutions, involving matrix factorizations, has been
developed to associate a quiver to a singularity. In this paper, we put
together these ideas to produce new AdS$_5$/CFT$_4$ duals, with special
emphasis on non-toric singularities.
