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The K-theory of uniform Roe algebras for coarse structures generated by finite-rank free abelian subgroups
Charles Fanning, Mehmet Emin Aktas
For a uniformly locally finite coarse space , the uniform Roe algebra is the operator norm closure of the controlled operators on . The -theory of unifo…
On the Spectral Synthesis of Lipschitz Vectorizations of Persistence Diagrams
Charles Fanning, Mehmet Emin Aktas
Persistence diagrams are fundamental descriptors in topological data analysis. Many statistical and machine learning methods require persistence diagrams to be mapped into vector s…
Square Metric Spaces
Charles Fanning, Mehmet Aktas
Product decompositions of metric spaces are built from coordinate maps, but these maps are not part of the resulting metric space. We recover this missing coordinate structure thro…
Higher-order Persistence Diagrams
Charles Fanning, Mehmet Aktas
Many topological data analysis (TDA) pipelines compute large collections of persistence diagrams, yet vectorizations and kernel methods discard the rank-induced implication relatio…
Random Walks on Virtual Persistence Diagrams
Charles Fanning, Mehmet Aktas
In the uniformly discrete case of virtual persistence diagram groups , we construct a translation-invariant heat semigroup. The kernels are supported on a countable subgrou…