Stability of 2-Parameter Persistent Homology
Explore a comprehensive lecture on the stability of 2-parameter persistent homology presented by Michael Lesnick. Delve into the natural analogues of standard stability results for union-of-balls, Čech, and Rips persistent homology in the 2-parameter setting, with a focus on multicover bifiltration and Sheehy's subdivision bifiltrations. Discover how these findings demonstrate the robust nature of these bifiltrations, particularly their stability against outliers. Examine stability results for degree bifiltrations, noting their relative weakness but tightness. Learn about the computational aspects of the studied bifiltrations and their implications for practical 2-parameter persistence development. If time allows, gain insights into related work on ℓp-type stability results for 2-parameter persistence. This 55-minute talk primarily covers joint work with Andrew Blumberg, while also touching on collaborations with Håvard Bjerkevik, René Corbet, Michael Kerber, Georg Osang, and Roy Zhao.