Two k-element subsets I,J of {1,2,…,n} are weakly separated if the sets I\J and J\I (when drawn on a circle with vertices 1,2,…,n) can be separated by a chord. A maximal weakly separated collection is a set of pairwise weakly-separated k-element subsets of {1,2,…,n} that is not contained in any larger set with this property. This definition gives rise to natural combinatorial questions: How big is a maximal weakly separated collection? How many are there? How are they related to each other?

I will outline how Oh, Posknikov, Speyer answered most of these questions via a bijection between maximal weakly separated collections in a positroid and move-equivalent plabic graphs. Along the way, we’ll meet some fun combinatorial objects related to plabic graphs including bounded affine permutations, Grassmann necklaces, positroids, and plabic tilings.