Counting Embedded Spheres with the Same Persistence

Explore a 34-minute conference talk that delves into the extension of collaborative work on inverse problems in Topological Data Analysis. Learn about a closed-form formula for counting unbraided height equivalence classes of embedded two-spheres with a prescribed level-set barcode. Discover how this research, conducted by Justin Curry and PhD student Jordan DeSha, establishes a conjecture from earlier work. Gain insights into topics such as the Eldar rule, merge trees, and graph equivalence. Follow the presentation's structure, which includes an introduction, review of inverse problems, and a dedicated question session at the end.