Alex Elchesen - Research

My broad research interests are in topology, optimal transport, and data analysis. More specifically, I'm interested in both theory and applications of topological data analysis, optimal transport and its intersection with TDA, and functional analytic aspects of optimal transport.

Preprints

Anti-Vietoris-Rips Metric Thickenings and Borsuk Graphs

with Henry Adams, Sucharita Mallick, and Michael Moy

Relative Optimal Transport

with Peter Bubenik

A Categorical Approach to Möbius Inversion via Derived Functors

with Amit Patel

Learning on Persistence Diagrams as Radon Measures

with Iryna Hartsock, Jose Perea, and Tatum Rask

Publications

Virtual Persistence Diagrams, Signed Measures, Wasserstein Distances, and Banach Spaces

with Peter Bubenik

Journal of Applied and Computational Topology, 1-46. 2022.

[Arxiv, Journal]

Universality of Persistence Diagrams and the Bottleneck and Wasserstein Distances

with Peter Bubenik

Computational Geometry, 105, 101882. 2022.

[Arxiv, Journal]

Topological Data Analysis of C. elegans Locomotion and Behavior

with Ashleigh Thomas, Kathleen Bates, Iryna Hartsock, Hang Lu, and Peter Bubenik

Frontiers of Artificial Intelligence. 2021.

[Arxiv, Journal]

The Reflection Distance Between Zigzag Persistence Modules

with Facundo Mémoli

Journal of Applied and Computational Topology, 185-219. 2019.

[Arxiv, Journal]

PhD Thesis

Universality of the Wasserstein Distances and Relative Optimal Transport

Advised by Peter Bubenik

[UF Digital Collections]

Master's Thesis

Stability of Zigzag Persistence with Respect to a Reflection-type Distance

Advised by Facundo Mémoli

© 2025 Alex Elchesen

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