An Intrinsic Persistent Homology Transform

Explore an in-depth lecture on the Intrinsic Persistent Homology Transform (IPHT) and its applications in topological data analysis. Delve into the origins of the Persistent Homology Transform (PHT) and Euler Characteristic Transform (ECT), understanding their significance as the first TDA invariants proven to be injective on shapes embedded in Euclidean space. Examine recent developments in the field, including new proofs, finiteness results, and practical applications. Focus on joint research with Steve Oudot, investigating an analogue of these constructions for intrinsic metric spaces, particularly metric graphs. Discover the unique properties of the IPHT, including its lack of injectivity in certain cases and its generic injectivity in appropriate topologies. Gain insights into the evolving landscape of algebraic topology and its implications for shape analysis and data science.