Atish Mitra

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math.AT2026

The Intersection Euler Characteristic Profile: Euler Calculus and Stability for Topological Interaction of Ball Unions

Kazuhiro Kawamura, Sushovan Majhi, Atish Mitra

The Intersection Euler Characteristic Profile (Intersection ECP) of $k$ colored point clouds $X_{1}, \dots, X_{k} \subset R^{d}$ is the Euler characteristic $χ(\bigcap_{i=1}^k…

math.AT2026

Vietoris--Rips Shadow for Euclidean Graph Reconstruction

Rafal Komendarczyk, Sushovan Majhi, Atish Mitra

The shadow of an abstract simplicial complex $K$ with vertices in $R^{N}$ is a subset of $R^{N}$ defined as the union of the convex hulls of simplices of $K$ . The Vie…

math.AT2026

The Shadow of Vietoris--Rips Complexes in Limits

Kazuhiro Kawamura, Sushovan Majhi, Atish Mitra

The Vietoris-Rips complex, denoted $R_{I^}^{2} (X)$ , of a metric space $(X, d)$ at scale $I^^{2}$ is an abstract simplicial complex where each $k$ -simplex corresponds to $(k + 1)$ points of $X$ …