Rocío Gonzalez Diaz: Fuzzy Simplicial Homology: A Step Towards Fuzzy Topological Data Analysis
Time: Thu 2026-05-28 15.15 - 15.45
Location: KTH 3721, Lindstedtsvägen 25 and Zoom
Video link: https://kth-se.zoom.us/j/65583358144?pwd=us6mdDtBgkEdZefvgbZPBWNujl3YuJ.1
Participating: Rocío Gonzalez Diaz (University of Sevilla)
Abstract.
Simplicial homology is a classical tool that assigns a sequence of modules to a simplicial complex, providing invariants for the study of its topological properties. In this article, we introduce the notion of L-fuzzy simplicial homology, a generalization of simplicial homology for L-fuzzy subcomplexes, in which each simplex is assigned a value from a completely distributive lattice L. We present its definition and main properties and describe methods to compute its structure. In addition, we interpret filtrations over a poset and chromatic datasets in this setting, opening a door to further applications in topological data analysis. For more information, please visit https://arxiv.org/abs/2604.08166