Tropical disks counting, stability conditions in symplectic geometry and quiver representations

Man-Wai, Mandy, Cheung (Harvard University)

Wednesday 2nd December, 2020 16:00-17:00 online zoom


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 A2 quiver. It is known that the derived Fukaya-Seidel category of the rational elliptic surface is the derived category of the A2 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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