High-density QCD is a new frontier in the investigation of the QCD phase diagram. The theoretical study of the "condensed matter physics" of QCD has led to several surprising discoveries, such as robust color superconducting phases and a new color-flavor-locked phase of quark matter. There are many important problems that remain to be studied. We would like to understand how to combine perturbative QCD and effective field theory techniques in order to perform systematic studies of the phase diagram and the structure of matter at high baryon density. We would like to systematically build in correlations that correspond to the formation of nucleons at moderate density. At even lower density we would like to see whether one can gain additional insights into the traditional nuclear matter problem using methods such as the renormalization group.

Ultimately, many interesting questions will have to be settled with the help of numerical simulations on the lattice. Currently this is not feasible because standard simulation methods suffer from the fermion sign problem. Recently, important progress was made in simulating QCD for non-zero temperature and small chemical potential. These simulations are based on improved reweighting methods or analytic continuation from imaginary chemical potential. We plan to bring together experts in lattice QCD and analytical methods in order to assess the status, the range of applicability, and limitations of the current simulation methods. We wish to discuss how these methods can be extended to larger chemical potential and smaller temperature. Methods such as the reweighting technique present an important practical step forward, but fall short of being a true solution of the sign problem. We also wish to discuss ideas that may eventually lead to solutions of the sign problem.

Compact stars are the only physical objects in which cold and dense baryonic matter is realized in nature. Neutron star observations have always provided important constraints on the nuclear equation of state. Today, a new generation of X-ray satellites such as Chandra and XMM-Newton, as well as the Rossi XTE, is providing an unprecedented wealth of data on the spectra of neutron stars. As a result, we expect significant further information on neutron star masses, radii, long term cooling and possible exotic internal states, surface composition, and physics in strong gravity, to emerge. Other important observables are the spin evolution of neutron stars, including short term time variability (glitches) which provide information on internal states of superfluidity, and possible observations of the neutrino burst from a nearby supernova.

One of our objectives is to bring together experts on the structure and evolution of neutron stars as well as theorists who study the high density phase of QCD. We also plan to invite observers in order to discuss recent findings. We wish to critically examine the question how neutron stars can serve as useful laboratories to address the high density phase of QCD and to identify the observables that hold the most promise in this regard.