Speaker: Qiyue Chen

Title: Scattering diagrams for closed surfaces

Abstract: Cluster scattering diagrams have been introduced by Gross-Hacking-Keel-Kontsevich from homological mirror symmetry, and shortly afterwards, stability scattering diagrams have been introduced by Bridgeland from the view of representation theory. Aiming at providing alternative ways to understand cluster algebra, it is fundamental to ask whether these two scattering diagrams are equivalent, with an affirmative answer provided by Bridgeland himself in acyclic cases, and later by Qin in injective-reachable cases. It remains to determine whether the equivalence still holds in non-injective-reachable cases, where we construct an example from the cluster algebra theory for surfaces, in which the stability and cluster scattering diagram are not equivalent. We also found evidence that the stability scattering diagram is more coherent with cluster algebra aspects in this example. This is a joint work with Qin Fan and Travis Mandel.