Singularity avoidance by collapsing shells in quantum gravity

We discuss a model describing exactly a thin spherically symmetric shell of matter with zero rest mass. We derive the reduced formulation of this system in which the variables are embeddings, their conjugate momenta, and Dirac observables. A non-perturbative quantum theory of this model is then constructed, leading to a unitary dynamics. As a consequence of unitarity, the classical singularity is fully avoided in the quantum theory.