**The Phase Diagram of QCD**

The long-term goal of this project is to determine from first principles the properties of quantum chromodynamics (QCD) as a function of the temperature and the densities of the u, d, and s quarks. A similar effort from experimental physicists is under way at particle accelerators RHIC and LHC, by colliding heavy ions. Theoretical progress is hampered by the “sign problem”: the fermion determinant becomes complex when the quark density (or equivalently the quark chemical potential) is non-zero, which makes the usual Monte Carlo sampling impossible. These researchers have been pursuing, very successfully, the strategy of making the chemical potential mu imaginary. Positivity of the determinant is restored, and standard Monte Carlo can be used. The imaginary-mu results can be analytically continued to real mu. Moreover, the critical points found at imaginary mu imply scaling laws extending to real mu. Thus, the researchers want to constrain the real-mu properties, by pinning down the phase diagram for imaginary-mu, accumulating more knowledge by letting the quark masses take arbitrary values. These simulations of lattice QCD with imaginary chemical potential are quite standard. The researchers are determining the critical surfaces and tricritical lines in the extended phase diagram by well-established finite-size scaling techniques. Computing resources are absorbed in the simulation of large systems near criticality.