How to choose informative representations of topological features in persistent homology

Persistent homology has emerged as a powerful tool for understanding complex data. However, interpretation and proper use of persistent shape statistics often hinges on a (theoretically) intractable inverse problem: selection of "good" cycles to represent features in homology. In this talk we will recall the basic notions of persistent homology and some of its recent scientific applications. We'll discuss what makes a cycle representatives better or worse in this context, and show experimental evidence that "guessing" reliably produces good representatives. We'll then explore some beautiful and interesting properties of optimal cycles observed in scientific data.

This talk will be hybrid, held in-person and online on Zoom