Chiral symmetry and the spectrum of the QCD Dirac operator

According to the Banks-Casher formula the chiral order parameter is directly related to the spectrum of the Dirac operator. In this lecture, we will argue that some properties of the Dirac spectrum are universal and can be obtained from a random matrix theory with the global symmetries of the QCD partition function. In particular, this is true for the spectrum near zero on the scale of a typical level spacing. Alternatively, the chiral order parameter can be characterized by the zeros of the partition function. We will analyze such zeros for a random matrix model at nonzero chemical potential.