This lecture will start with some background on Hilbert complexes, ideal boundary conditions and self-adjointness for unbounded operators on singular spaces. We will then introduce a fundamental theorem about the pseudo differential cone calculus and show how this theorem may be used to study these issues on spaces with conical singularities. We will finish with a discussion of how the analytic obstructions in this setting relate to the topological obstruction to the existence of a unique middle perversity intersection cohomology.