Brittany Terese Fasy

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  Finite Representations of Shapes in Euclidean Space
  Brittany Terese Fasy
  The persistence diagram is a topological summary that is gaining traction as a (directional) descriptor of shapes in Euclidean space. Recent work has shown that well-chosen (finite) sets of diagrams can differentiate between geometric simplicial complexes, providing a method for representing shapes using a finite set of topological descriptors. A related inverse problem is the following: given an oracle we can query for persistence diagrams, what is underlying geometric simplicial complex? This talk will explore the representation of simplicial complexes by parameterized families of persistence diagrams, along with the inverse problem of how to recover the initial simplicial complex.