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math.AT2026
On the support of Betti tables of multiparameter persistent homology modules
Andrea Guidolin, Claudia Landi
Persistent homology encodes the evolution of homological features of a multifiltered cell complex in the form of a multigraded module over a polynomial ring, called a multiparamete…
math.AT2024
Algebraic Wasserstein distances and stable homological invariants of data
Jens Agerberg, Andrea Guidolin, Isaac Ren +1
Distances have a ubiquitous role in persistent homology, from the direct comparison of homological representations of data to the definition and optimization of invariants. In this…
math.AT2024
Koszul complexes and relative homological algebra of functors over posets
Wojciech Chacholski, Andrea Guidolin, Isaac Ren +2
Under certain conditions, Koszul complexes can be used to calculate relative Betti diagrams of vector space-valued functors indexed by a poset, without the explicit computation of…