On the paper ,,Stability of Persistence Diagrams" by D. Cohen-Steiner, H. Edelsbrunner and J. Harer

The goal of the talk is to describe the contents of paper mentioned in the title. This interesting paperaddresses a number of topics. First, it introduces an analogue of a Morse function in the setting of topological spaces (tame functions), and shows that the main consequences of Morse theory still hold in this setting. Next the authors describe how persistent homology groups naturally appear. Finally the authors prove a number of stability results: appropriately defined distance between the persistence diagrams (points in the plane whose coordinates give the birth and death of  a generator in persistent homology) of two tame functions is bounded from above by the supremum distance between these functions.