  The partition functions of QCD2 on simple surfaces admit representations in
terms of exponentials of the inverse coupling, that are modular transforms of
the usual character expansions. We review the construction of such a
representation in the case of the cylinder, and show how it leads to a
formulation of QCD2 as a $c=1$ matrix model of the Kazakov-Migdal type. The
eigenvalues describe the positions of $N$ Sutherland fermions on a circle,
while their discretized momenta label the representations in the corresponding
character expansion. Using this language, we derive some new results: we give
an alternative description of the Douglas-Kazakov phase transition on the
sphere, and we argue that an analogous phase transition exists on the cylinder.
We calculate the large $N$ limit of the partition function on the cylinder with
boundary conditions given by semicircular distributions of eigenvalues, and we
find an explicit expression for the large $N$ limit of the Itzykson-Zuber
integral with the same boundary conditions. (Talk given at the ``Workshop on
high energy physics and cosmology'' at Trieste, July 1993.)
