Scattering diagrams from holomorphic discs in log Calabi-Yau surfaces

Scattering diagrams from holomorphic discs in log Calabi-Yau surfaces Lin, Yu-Shen; Bardwell-Evans, Sam; Cheung, Man-Wai Mandy; Hong, Hansol We construct special Lagrangian fibrations for log Calabi-Yau surfaces, and scattering diagrams from Lagrangian Floer theory of the fibres. Then we prove that the scattering diagrams recover the scattering diagrams of Gross-Pandharipande-Siebert and the canonical scattering diagrams of Gross-Hacking-Keel. With an additional assumption on the non-negativity of boundary divisors, we compute the disc potentials of the Lagrangian torus fibres via a holomorphic/tropical correspondence. As an application, we provide a version of mirror symmetry for rank two cluster varieties.