Computing the Matching Distance of Bi-Persistence Modules

Explore theoretical advances in computing the matching distance between bi-persistence modules through this 55-minute conference talk from the Applied Algebraic Topology Network. Discover how to exactly compute the matching distance between two "nice" bi-persistence modules using collaborative research findings with Claudia Landi, Asilata Bapat, Barbara Mahler, Celia Hacker, and Elizabeth Stephenson. Learn that the matching distance between tame bi-persistence modules M and N can be computed using finitely many lines in parameter space, determined by a finite set of points in R² consisting of critical parameter values (where homology of M and/or N changes) and switch points (where optimal matching determining bottleneck distance along lines may change). Examine the practical implementation of these theoretical results and review experimental outcomes demonstrating the effectiveness of this computational method for bi-persistence modules in applied algebraic topology.