Anna Schenfisch (Dept. of Mathematical Sciences, MSU) 

10/21/2021  3:10pm

Abstract: 

In this talk, we discuss a finite set of persistence diagrams that retains the information of an uncountably infinite set of persistence diagrams, also known as the Persistent Homology Transform (PHT). The diagrams in question are generated by lower-star filtrations over some fixed simplicial complex. The discussion will be geometrically focused and show how our finite set of diagrams can be used to reconstruct the underlying simplicial complex, proving that the set is a faithful discretization of the PHT. 

 

Although investigating the PHT through the lens of reconstruction is more strict than necessary for discretization, this method yields bounds that are improvements from those previously known.