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From Higher Invariants

Jacob Leygonie (Oxford): The fiber of Persistent Homology

Abstract: Persistent Homology (PH) is a central descriptor in Topological Data Analysis (TDA) that encodes the topological properties of a real-valued function on a space by means of its sub-level sets. But in fact it remains mysterious what information is really captured by PH and what information is lost; formally this means that the fiber of PH is not understood. Apart from its relevance to the numerous applications of Persistent Homology, we will see that this fiber is a beautiful object.