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math.AT2025
Persistence and Topological Complexity
Facundo Mémoli, Ling Zhou
Topological complexity is a homotopy invariant that measures the minimal number of continuous rules required for motion planning in a space. In this work, we introduce persistent a…
math.CO2025
Grassmannian Persistence Diagrams: Special Properties in the 1-Parameter Setting
Aziz Burak Gülen, Facundo Mémoli, Zhengchao Wan
In this paper, we explore the discriminative power of Grassmannian persistence diagrams of 1-parameter filtrations, examine their relationships with other related constructions, an…
math.AT2025
-Stability of Weighted Persistence Diagrams
Aziz Burak Gülen, Facundo Mémoli, Amit Patel
We introduce the concept of weighted persistence diagrams and develop a functorial pipeline for constructing them from finite metric measure spaces. This builds upon an existing fu…