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math.AT2026★ 1 cited
Galois Connections in Persistent Homology
Aziz Burak Gulen, Alexander McCleary
We present a new language for persistent homology in terms of Galois connections. This language has two main advantages over traditional approaches. First, it simplifies and unifie…
math.AT2024
Edit Distance and Persistence Diagrams Over Lattices
Alexander McCleary, Amit Patel
We build a functorial pipeline for persistent homology. The input to this pipeline is a filtered simplicial complex indexed by any finite metric lattice and the output is a persist…