  We review our recent measurements of the complex AC conductivity of thin
InO_x films studied as a function of magnetic field through the nominal 2D
superconductor-insulator transition. These measurements - the first of their
type to probe nonzero frequency - reveals a significant finite frequency
superfluid stiffness well into the insulating regime. Unlike conventional
fluctuation superconductivity in which thermal fluctuations give a
superconducting response in regions of parameter space that don't exhibit long
range order, these fluctuations are temperature independent as T --> 0 and are
exhibited in samples where the resistance is large (greater than 10^6
Ohms/Square) and strongly diverging. We interpret this as the direct
observation of quantum superconducting fluctuations around an insulating ground
state. This system serves as a prototype for other insulating states of matter
that derive from superconductors.
