what is the significance of the title "the ministers vigil"

Dimmesdale holds his vigil at the scaffold where Hester Prynne suffered her public humiliation several years prior. This is the spot where Dimmesdale feels his hidden shame most acutely. While Hester was punished for her adultery on the scaffold, Dimmesdale hid his own sin and shame. Dimmesdale is attempting to purge the sins that weigh heavy on his heart.