Lin, Yu-ShenBardwell-Evans, Sam A.Cheung, Man-WaiHong, Hansol2022-04-292022-04-29Y.-.S. Lin, S. Bardwell-Evans, M.-.W. Cheung, H. Hong. "Scattering diagrams from holomoprhic discs in log Calabi-Yau surfaces."https://hdl.handle.net/2144/44324We 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.en-USThis version of the work is distributed under a Creative Commons Attribution 4.0 licence. Add to end of citation: https://arxiv.org/abs/2110.15234http://creativecommons.org/licenses/by/4.0/Article713512