Generalizing the interleaving distance using categorical flows

Interleaving distance is a measure of similarity between persistence modules and it's been a central concept in algebraic topology and topological data analysis. Through a guiding example, this video introduces categorical flows—a functorial operation that extends the interleaving distance into a measure between objects of virtually any category. This video is part of the tutorial-a-thon 2025 Spring by the Applied Algebraic Topology Research Network (AATRN)

Revealing brain network dynamics during the emotional state of suspense using topological data analysis

We applied a tool from Topological Data Analysis (TDA) Mapper , to find the relation of brain dynamics and suspense. As result, we found changes in the functional connectivity within and between large-scale networks associated with the level of suspense. This is master's thesis , supervised by Professors Francisco Gomez and Jose Perea See Papers for the preprint version.

Persistent Homology for clusterization of RNA secondary structures

As part of my bachelor's thesis I worked with Professors Gustavo Rubiano and Clara Bermudez applying persistent homology to cluster RNA secondary structures. We interpreted the 0-homology classes (connected-components) as clusters, resulting a method comparable to hierarchical clustering.

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