Justin Curry, Justin Curry
This talk will begin with a review of elementary constructions in topological data analysis (TDA), such as merge trees and the Elder Rule. A brief introduction to inverse problems in TDA is considered before turning to recent joint work with Catanzaro, Fasy, Lazovskis, Malen, Reiss, Wang and Zabka in https://arxiv.org/abs/1909.10623. The talk will conclude with recent combinatorial results obtained by my PhD student, Jordan DeSha, who provided a closed-form formula for the number of unbraided height equivalence classes (HECs) of embedded two-spheres with a prescribed level-set barcode. This formula establishes a conjecture outlined in the earlier paper with Catanzaro, et al.
