Richard P. Stanley Seminar in Combinatorics
Building 2, Room 132, 182 Memorial Drive, Cambridge, MA
Speaker: Lang Mou (UC Davis) Title: Leafy trees, wall-crossing, and m-Tamari intervals Abstract: Trees appear in several approaches to wall-crossing. I will present a new plane-tree model for the central wall in rank-2 cluster scattering diagrams, inspired by the recently introduced tight gradings on Dyck paths. These trees turn out to be in bijection with intervals in the m-Tamari lattice, a lattice on m-ballot paths. I will explain this correspondence and show how the tree perspective leads to algebraic functional equations for enumerating these intervals and a new combinatorial proof of the central wall formula. No prior knowledge of wall-crossing or cluster algebras will be assumed. This talk is based on joint work with Amanda Burcroff and Kyungyong Lee.