  We discuss rapidly rotating states of a superfluid. We concentrate on the
Giant-Vortex (GV) state, which is a coherent rotating solution with a
macroscopic hole at the center. We show that, for any trap, the fluctuations
obey an approximately chiral dispersion relation, describing arbitrary shape
deformations moving with the speed of the ambient superfluid. This dispersion
relation is a consequence of a peculiar infinite symmetry group that emerges at
large angular velocity and implies an infinite ground-state degeneracy. The
degeneracy is lifted by small corrections which we determine both for smooth
traps and the hard trap.
