If we take an ultra-short distributional pulse of
gravitational radiation, the wavefront will move along a co-dimension
one light-like (null) surface in spacetime. The question of how to
describe the quantum geometry of such impulsive null initial data is a
significant problem shared across different approaches to quantum
gravity, from holography, celestial amplitudes, to loop quantum gravity
and quantum Regge calculus. In my presentation, I report on three new
results on this frontier. First, a new mathematical technique is
introduced to characterize the phase space of the radiative modes of
such a pulse at the full non-perturbative level. Second, the description
is taken to the quantum level. Third, an immediate physical implication
is found: in the model, the Planck luminosity separates the eigenvalues
of the radiated power. Below the Planck power, the spectrum of the
radiated power is discrete. Above the Planck power, the spectrum is
continuous and the resulting physical states contain caustics that can
spoil the semi-classical limit. The talk is based on arXiv:2402.12578,
arXiv:2401.17491, arXiv:2104.05803.