Collapsing Higher Order Čech to Higher Order Delaunay Complexes - Current Results and Open Questions

Explore the relationship between higher order Čech and Delaunay complexes in Topological Data Analysis (TDA) through this insightful lecture. Delve into the extension of these simplicial complexes to their higher order versions, which offer enhanced robustness in handling outliers. Learn about the ongoing research on relating these complexes through simplicial collapses, focusing on the concept of t-Voronoi regions. Gain understanding of the explicit collapsing sequence derived from this approach and examine the current results and open questions in this field of study. Discover the potential implications of this work for more effective analysis of finite point sets in TDA.