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math.AT2026
Choosing the Geometry: valuations, norms, and contours
Jens Agerberg, Wojciech Chachólski, Christina Kapatsori
We develop a general framework for constructing pseudometrics on objects of Abelian categories using valuations, which assign non-negative costs to morphisms. Specializing to finit…
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…