In this talk, I will talk about the SYZ-mirror symmetry of immersed Lagrangian multi-sections of a semi-flat torus fibration. We will introduce the notion of lifted-Hamiltonian isotopy, which is the mirror analog for isomorphism of holomorphic bundles. Furthermore, the Floer cohomology for a pair of immersed Lagrangian multi-sections turns out to be invariant under this new notion of equivalence. Finally, I will focus on the 2-torus and study the relation between Lagrangian surgery and extension of holomorphic bundles there.
