Posets of Topological Descriptors
Talk by Anna Schenfisch (Mathematical Sciences, MSU)
04/12/2021 4:10pm Zoom Meeting
Given a general simplicial complex embedded in R^d, there exist finite sets of topological descriptors (persistence diagrams, etc.) that fully represent the complex. These sets have an interesting connection to a particular stratification of the sphere. By comparing the cardinalities of such sets for different topological descriptor types, we build a framework through which descriptor types can be ordered. We then partially order six common descriptor types as a case study, as well as describe a construction of a simplicial complex that requires surprisingly many augmented descriptors to form a representation. Throughout, we will pause to note research highlights as well as proposed work and conjectures.