Hypergraph homologies (BONUS: ECT for paleontology and the origin of life)

Date

Mar 5, 2026

Time

3:00 PM - 4:00 PM

Speaker

Bernat Jordà Carbonell

Affiliation

VU Amsterdam

Language

en

Main Topic

Biologie

Host

Local Organisers: Nikola Sadovek, Maximilian Wiesmann, Giulio Zucal

Description

Hypergraphs extend graphs and simplicial complexes by representing higher-order interactions with more degrees of freedom. However, the absence of downward closure makes the usual chain-level boundary operators fail. How to get around this is not trivial and different authors have proposed different approaches that get to completely different homologies. While trying to better understand what information is relevant from the hypergraphs, we notice that one of the most promising homology theories (relative barycentric homology) is equivalent to the compact support homology of our geometric realisation of a hypergraph. We prove a natural isomorphism between these homologies and determine the functoriality of the former. BONUS: How can we adapt TDA tools generally used for biology to paleontology? In Paleo we don’t have access to 3d structures, only images of sections of rock that might be degraded and transformed after such a long time. More specifically, if we want to bring life to the scientific discussion on origins of life, we need to look at fossils of bacteria. The small scale and degradation makes this task quite complicated and the use of morphometry has not been applied successfully (yet!).

Last modified: Mar 5, 2026, 7:39:28 AM