Parallel Decomposition of Persistence Modules Through Interval Bases

Explore a groundbreaking algorithm for decomposing finite-type persistence modules with field coefficients into interval bases in this 50-minute talk by Francesco Vaccarino. Delve into the construction of this algorithm, which not only yields standard persistence pairs in Topological Data Analysis (TDA) but also generates a special set of generators for the interval decomposition of the Structure theorem. Learn how this computation can be distributed across persistence module steps and how it applies to general persistence modules on a field, beyond persistent homology. Discover a parallel algorithm for building persistent homology modules using the Hodge decomposition, offering new insights into the relationship between TDA and the Hodge Laplacian. Gain valuable knowledge from this collaborative research presented by the Applied Algebraic Topology Network, based on work with Alessandro De Gregorio, Marco Guerra, and Sara Scaramuccia.