  Making combined use of the Matrix and Maldacena conjectures, the relation
between various thermodynamic transitions in super Yang-Mills (SYM) and
supergravity is clarified. The thermodynamic phase diagram of an object in DLCQ
M-theory in four and five non-compact space dimensions is constructed; matrix
strings, matrix black holes, and black $p$-branes are among the various phases.
Critical manifolds are characterized by the principles of correspondence and
longitudinal localization, and a triple point is identified. The microscopic
dynamics of the Matrix string near two of the transitions is studied; we
identify a signature of black hole formation from SYM physics.
