Alfred Mueller is the Enrico Fermi Professor of Physics at Columbia University. His current research centers on the properties of QCD systems at very high density. Such systems occur in high-energy heavy ion collisions and are also measured in high-energy (small x) deep inelastic lepton-proton scattering. Topics Mueller has been particularly interested in are: (i) The relationship between unitarity limits and parton density limits (saturation); (ii) The maximal allowed occupation numbers for quarks and gluons in an hadronic wavefunction; (iii) First principles calculation of the approach to equilibration using a Boltzmann equation or(equivalently) classical Yang-Mills equations; (iv) The relationship between the factorial divergence of the QCD perturbation series and high field strength configurations. (v) The relationship between saturation phenomena in QCD and the reaction-diffusion processes in statistical physics.