Multiparameter Persistence

As a postdoc, I began work on geometric models for studying multiparameter persistence. One of the first examples of ordinary persistence arose from studying the sub-level sets of a Morse function. Together with Peter Bubenik, we propose looking at generic families of Morse functions to study multiparameter persistent homology. Using tools from geometric topology, we attempt to build a decomposition of the associated multiparameter persistence module, analogous to the barcode.