Persistent homology and the stability theorem

Persistent homology, the homology of a filtration of topological spaces, is described up to isomorphism by the persistence diagram (barcode), which encodes the structure of its indecomposable summands. The stability theorem, a fundamental theorem in the theory of persistence, states that small changes in the input data lead only to small changes in the persistence barcode. We will explore a constructive algebraic approach to this result that admits a high level of generality.