  The propagation of long-wavelength gluons through a dense QCD medium at high
baryon chemical potential mu_B is qualitatively modified by the effects of
screening, arising from scatterings off the high-momentum quarks in the medium.
This same screening phenomenon also impacts gluons occurring in loop
corrections to the pressure of cold quark matter, leading to contributions from
the parametric scale Sqrt(alpha_s)*mu_B, starting at next-to-next-to-leading
order (N2LO) in the strong coupling constant alpha_s. At
next-to-next-to-next-to-leading order (N3LO), interactions between these
long-wavelength gluonic modes contribute to the pressure. These interaction
corrections have recently been computed in arXiv:2103.07427 and
arXiv:2103.05658, and the inclusion of these interactions slightly improves the
convergence of the equation of state of cold quark matter. In these
proceedings, we present these results and provide details summarizing how this
lengthy calculation was performed.
