This research studies the effects of brain stimulation (transcranial magnetic stimulation, or "TMS") on balance in progressive supranuclear palsy (PSP). The purpose of this research is to look for improvements in balance when subjects are on a tilting platform after stimulating the brain with a magnetic wand held over the scalp over an area at the back of the brain called the cerebellum. Participants will receive both active and inactive stimulation during the course of the study. There is no surgery involved. There are also optional portions of the study that include functional magnetic resonance imaging (fMRIs) and speaking samples.