in 1995, gessel introduced a multivariate formal power series $g$ tracking the distribution of ascents and descents in labeled binary trees. in addition to showing the $g$ is a symmetric function, he conjectured that $g$ is schur-positive. in this talk, we'll see how to expand $g$ positively in terms of ribbon schur functions. moreover, we'll see how certain specializations of $g$ relate to actions on hyperplane arrangements. as an application of our work, we get a proof of gamma-positivity of the distribution of right edges over the set of local binary search trees.