Algebraic Geometry Seminar: "Family Floer mirror and mirror symmetry for rank 2 cluster varieties"

Abstract: The Gross-Hacking-Keel mirror is constructed in terms of scattering diagrams and theta functions. The ground of the construction is that scattering diagrams inherit the algebro-geometric analogue of the holomorphic disks counting. With Yu-shen Lin, we made use of this idea and gave the first non-trivial examples of family Floer mirrors. Then with Sam Bardwell-Evans, Hansol Hong, and Yu-shen Lin, we construct a special Lagrangian fibration on the non-toric blowups of toric surfaces that contains nodal fibres, and prove that the fibres bounding Maslov 0 discs reproduce the scattering diagrams. As a consequence, we can then illustrate the mirror duality between the A and X cluster varieties.

Host: Ben Wormleighton