Non-diplaceable toric fibers on compact toric manifolds via tropicalizations

In this thesis, we give a combinatorial way to locate non-displaceable Lagrangian toric fibers on compact toric manifolds. By taking the intersection of certain tropicalizations coming from combinatorial data of the moment polytope, we locate all strongly bulk-balanced toric fibers. As an application, we show that every bulk-balanced fiber is strongly bulk-balanced. Combining the results, we conclude that this combinatorial method indeed detects the positions of all non-displaceable toric fibers that can be detected by Lagrangian Floer theory on compact toric manifolds developed by Fukaya, Oh, Ohta, and Ono.