  The equation of state (EOS) of dense matter plays an important role in the
supernova phenomenon, the structure of neutron stars, and in the mergers of
compact objects (neutron stars and black holes). During the collapse phase of a
supernova, the EOS at subnuclear densities controls the collapse rate, the
amount of deleptonization and thus the size of the collapsing core and the
bounce density. Properties of nuclear matter that are especially crucial are
the symmetry energy and the nuclear specific heat. The nuclear
incompressibility, and the supernuclear EOS, play supporting roles. In a
similar way, although the maximum masses of neutron stars are entirely
dependent upon the supernuclear EOS, other important structural aspects are
more sensitive to the equation of state at nuclear densities. The radii,
moments of inertia, and the relative binding energies of neutron stars are, in
particular, sensitive to the behavior of the nuclear symmetry energy. The
dependence of the radius of a neutron star on its mass is shown to critically
influence the outcome of the compact merger of two neutron stars or a neutron
star with a small mass black hole. This latter topic is especially relevant to
this volume, since it stems from research prompted by the tutoring of David
Schramm a quarter century ago.
