Wall crossing and quiver representations

Cluster algebras were introduced to understand the canonical bases in semisimple Lie groups. Later,
Gross-Hacking-Keel-Kontsevich related scattering diagrams from mirror symmetry to cluster algebras.
They further proposed that the set of theta functions give the canonical bases for cluster algebras.
Using this linkage, we are going to see how the theory in quiver representation, namely Auslander-Reiten
theory, can been visualized on scattering diagrams. Furthermore, we will discuss how broken lines,
which are used to constructed theta functions, give stratifications for quiver Grassmannians.