  String theories with two dimensional space-time target spaces are
characterized by the existence of a ``ground ring'' of operators of spin
$(0,0)$. By understanding this ring, one can understand the symmetries of the
theory and illuminate the relation of the critical string theory to matrix
models. The symmetry groups that arise are, roughly, the area preserving
diffeomorphisms of a two dimensional phase space that preserve the fermi
surface (of the matrix model) and the volume preserving diffeomorphisms of a
three dimensional cone. The three dimensions in question are the matrix
eigenvalue, its canonical momentum, and the time of the matrix model.
