Abstract: June Huh proved in 2012 that the Betti numbers of the complement of a complex hyperplane arrangement form a log concave sequence. But what if the arrangement has symmetries, and we regard the cohomology groups not just as vector spaces, as representations of the symmetry group? The motivating example is the braid arrangement, where the complement is the configuration space of n points in the plane, and the symmetric group acts by permuting the points. I will present an equivariant log concavity conjecture, and explain how to use the theory of representation stability to prove infinitely many cases of this conjecture for configuration spaces.