Realizability of tropical curves and Lagrangian submanifolds

Tropicalization is a process by which we replace algebraic geometry with the geometry of piecewise linear (tropical) objects. One of the central questions in the field is when this process can be reversed: that is, when can we realize a tropical object with an honest algebraic one. In this talk, I'll discuss some recent work on the tropical to Lagrangian correspondence, and state under what conditions homological mirror symmetry allows us to transfer Lagrangian realizations into algebraic ones.