After completing their baseline assessment, participants randomized to this arm will initially take part in a 2-week TMS intervention. After the midpoint assessment and subsequent a 1-month washout, these participants will then complete a 2-week sham TMS period prior to their final assessment.

After completing their baseline assessment, participants randomized to this arm will initially take part in a 2-week sham TMS period. After the midpoint assessment and subsequent a 1-month washout, these participants will then complete a 2-week TMS intervention prior to their final assessment.

Aim 1: To determine the clinical effects of rTMS targeting the cerebellum on postural instability in PSP. The hypothesis to be tested is that TMS augmentation of cerebellar inhibition will improve cerebellum-dependent balance symptoms of PSP for a period of time sufficient to improve rehabilitation outcomes. The investigators will measure a battery of objective posturography metrics and other measures of motor control, including sway and center of pressure changes to backward tilt and forward translation.

Aim 2: We will use functional near infrared spectroscopy (fNIRS) to examine changes in motor and premotor cortical activity after cerebellar rTMS. The hypothesis to be tested is that premotor and motor cortical activity will decrease after cerebellar rTMS compared to sham TMS, reflecting improved cerebellar inhibition of the motor cortex after the intervention.

The primary endpoint is center of pressure shifts with tilt and with translation, and body sway in quiet stance.

functional near infrared spectroscopy of premotor and motor areas during balance testing

speech sample assessment conducted by investigator