Topological data analysis (TDA) is a new approach to analyzing complexdata which often helps reveal otherwise hidden patterns by highlightingvarious geometrical and topological features of the data. Persistenthomology is a key in the TDA toolbox. It measures topological featuresof data that persist across multiple scales and thus are robust withrespect to noise. Persistent homology has had many successfulapplications, but there is room for improvement. For large datasets,computation of persistent homology often takes a significant amount oftime. Several approaches have been proposed to try to remedy this issue,such as witness complexes, but those approaches present their owndifficulties.
Oleksandr Markovichenko’s thesis presentation on: Persistent cohomology of cover refinements
March 10, 2022 @ 3:00 pm – 4:00 pm