Abstract by Nickolas Callor
Concurrent persistent homology: an introduction
Persistent homology (PH) is a standard data analysis tool in the sciences, which has been popularized over the last decade (Zomorodian and Carlsson, 2005; Carlsson and Zomorodian, 2009; Lesnick, 2015; Allili et al., 2017; Chacholski et al., 2017; Otter et al., 2017; Wasserman, 2018;). We introduce Concurrent persistent homology (CPH) as an optimal middle-ground between PH and the more abstract, and difficult to apply, notion of multiparameter persistent homology (MPH). We present a brief overview of how these methods apply to real world data and then present several theorems regarding their mathematical properties.