juin 2026
| Intervenant : | Jānis Lazovskis |
| Institution : | University of Latvia |
| Heure : | 11h00 - 12h00 |
| Lieu : | 2L8 |
Ecologists interested in the large-scale properties of a particular species often consider the niche, a high dimensional space of environmental variables which are suitable (and have been observed) for the species. Sampling bias and computational requirements for inferential statistics complicate the analysis, and strong arguments are needed to counter common ecological assumptions of (simple) connectedness and convexity. In a classic application of topology to data, we take aim at some of these issues, in the sense of giving precise bounds for how much the persistent homology can change when transforming large data sets into more computable ones, while still reflecting the heuristic expectation for the "shape of a species." Specifically, we give bounds in the bottleneck distance for how the dimension zero persistence diagram changes when using barycentric subdivision and sparsification on the input data set, applying both the Vietoris--Rips and cubical complex constructions. These steps fit together into a flexible pipeline intended for use in ecological data analysis, with less of an effect from sampling bias and with outputs quantifying the connectedness and codimension 1 features. Our implementation of this pipeline uses methods from GUDHI and CGAL, and is available in C++, Python, and R. This work, joint with Ran Levi and Juliano Morimoto, is part of a larger program to supply ecology with topological tools, and is supported by the Latvian Council of Science grant 1.1.1.9/LZP/1/24/125.