Bridgeland developed stability scattering diagrams relating scattering diagrams with quiver representations. Scattering diagrams were developed as a machinery in mirror symmetry. Together with Travis Mandel, we associate tropical disks counting with quiver representations by using the stability scattering diagrams. Next, together with Yu-Wei Fan and Yu-Shen Lin, we look at the stable objects for the $A_2$ quiver. It is known that the derived Fukaya-Seidel category of the rational elliptic surface is the derived category of the $A_2$ quiver. We made use of the relation and corresponded the special Lagrangian with the stable objects in the derived category of coherent sheaves.
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