Sean Gryb (Radboud) gives a talk at the Workshop on the Problem of Time in Perspective (3-4 July, 2015) titled "In Favour of a Schrödinger Evolution of the Universe". Abstract: In the canonical formulation of reparametrization invariant systems, time evolution on phase space is generated by a fully constrained Hamiltonian. On the orthodoxy view, the quantum formalism for such systems is constructed through Dirac quantization, which leads to a real, time-independent constraint on the quantum state. The question then remains how to extract a notion of time evolution from this frozen formalism. On one predominant view, the system is to be split in terms of ''partial observables'' -- which may be used as internal clocks -- and a set of ''complete observables'' -- which are understood to evolve in terms of the former. This has led to a controversy around the interpretation of the partial observables within the formalism. In this talk, we will provide a negative argument against the orthodoxy view that clarifies the role that should be played by the partial observables. We then present a proposal for the canonical quantization of reparametrization invariant systems that naturally encodes a genuine notion of time evolution and illustrate how this proposal can be applied to gravity.