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math.AT2026
Topology of Multi-species Localization
Abhinav Natarajan, Thomas Chaplin, Joshua A. Bull +5
Spatial relationships in multi-species data can indicate and affect system outcomes and behaviors, ranging from disease progression in cancer to coral reef resilience in ecology; t…
math.AT2025
Morse theory for chromatic Delaunay triangulations
Abhinav Natarajan, Thomas Chaplin, Adam Brown +1
The chromatic alpha filtration is a generalization of the alpha filtration that can encode spatial relationships among classes of labelled point cloud data, and has applications in…
math.AT2024
A notion of homotopy for directed graphs and their flag complexes
Thomas Chaplin, Heather A. Harrington, Ulrike Tillmann
Directed graphs can be studied by their associated directed flag complex. The homology of this complex has been successful in applications as a topological invariant for digraphs.…