Shreya Arya

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math.AT2025

Kan Approximations of the Persistent Homology Transform

Shreya Arya, Justin Curry

The persistent homology transform (PHT) of a subset $M \subset R^{d}$ is a map $PHT (M) : S^{d - 1} \to Dgm$ from the unit sphere to the space of persist…

math.AT2024

Decomposing the Persistent Homology Transform of Star-Shaped Objects

Shreya Arya, Barbara Giunti, Abigail Hickok +3

In this paper, we study the geometric decomposition of the degree- $0$ Persistent Homology Transform (PHT) as viewed as a persistence diagram bundle. We focus on star-shaped objects…