  We use F. Ferrari's methods relating matrix models to Calabi-Yau spaces in
order to explain Intriligator and Wecht's ADE classification of $\N=1$
superconformal theories which arise as RG fixed points of $\N = 1$ SQCD
theories with adjoints. The connection between matrix models and $\N = 1$ gauge
theories can be seen as evidence for the Dijkgraaf--Vafa conjecture. We find
that ADE superpotentials in the Intriligator--Wecht classification exactly
match matrix model superpotentials obtained from Calabi-Yau's with
corresponding ADE singularities. Moreover, in the additional $\Hat{O}, \Hat{A},
\Hat{D}$ and $\Hat{E}$ cases we find new singular geometries. These `hat'
geometries are closely related to their ADE counterparts, but feature
non-isolated singularities. As a byproduct, we give simple descriptions for
small resolutions of Gorenstein threefold singularities in terms of transition
functions between just two coordinate charts. To obtain these results we
develop techniques for performing small resolutions and small blow-downs,
including an algorithm for blowing down exceptional $\PP^1$'s. In particular,
we conjecture that small resolutions for isolated Gorenstein threefold
singularities can be obtained by deforming matrix factorizations for simple
surface singularities -- and prove this in the length 1 and length 2 cases.
