Unitarity and quantum resolution of gravitational singularities

In trying to formulate quantum theories of gravity, we need to agree on which principles of quantum mechanics and general relativity are expected as fundamental in the new theory. One of the most important properties of standard quantum mechanics is unitarity of time evolution. Quantum gravity is often expected or required to be unitary in some sense, although it is less clear what that means. I will explore different ways in which unitarity could be realised in quantum models of cosmology and black holes, and in particular show that certain notions of unitarity seem to require resolution of all classical singularities.