Abstract：

Take an irrational rotation of the two-sphere; it only has the north and south poles as its periodic points. However, Franks proved that for any area-preserving diffeomorphism of the two-sphere, if it has more than two fixed points, then it must have infinitely many periodic points. I will discuss a generalization of this result with Guangbo Xu to all compact toric manifolds, for which the gauged linear sigma model (GLSM) plays a surprising role.