  We use computer simulations to study the glass transition of dense fluids
made of polydisperse, repulsive spheres. For hard particles, we vary the volume
fraction, phi, and use compressible particles to explore finite temperatures,
T>0. In the hard sphere limit, our dynamic data show evidence of an avoided
mode-coupling singularity near phi_{MCT} ~ 0.592, they are consistent with a
divergence of equilibrium relaxation times occurring at phi_0 ~ 0.635, but they
leave open the existence of a finite temperature singularity for compressible
spheres at volume fraction phi > phi_0. Using direct measurements and a new
scaling procedure, we estimate the equilibrium equation of state for the hard
sphere metastable fluid up to phi_0, where pressure remains finite, suggesting
that phi_0 corresponds to an ideal glass transition. We use non-equilibrium
protocols to explore glassy states above phi_0 and establish the existence of
multiple equations of state for the unequilibrated glass of hard spheres, all
diverging at different densities in the range phi \in [0.642, 0.664].
Glassiness thus results in the existence of a continuum of densities where
jamming transitions can occur.
