The 3d A-model and mirror symmetry

To a symplectic algebraic variety or stack, we should be able to associate a 3d A-model and B-model, which are equivalent to the B-model and A-model associated to some dual space. Boundary conditions for these are expected to form 2-categories whose objects are holomorphic Lagrangian submanifolds equipped with some extra data. There are many difficulties in defining these 2-categories, but we discuss some situations where expectations for them can be made precise, together with implications for 2d mirror symmetry. This is based on work with Justin Hilburn, including work with Aaron Mazel-Gee and ongoing discussions with Ahsan Khan.