Color superconductivity in ultra-dense quark matter

At ultra-high density, matter is expected to form a degenerate Fermi gas of quarks in which there is a condensate of Cooper pairs of quarks near the Fermi surface. This phenomenon is called color superconductivity. In these proceedings I review the underlying physics of color superconductivity and our current understanding of the possible phases of real-world quark matter. Then I consider how lattice gauge theorists would proceed to investigate the phase structure of dense quark matter if it were possible to perform the path integral numerically, i.e. if the sign problem had been solved.