27th of May - Bettina Speckman
3rd of June - Jean-Baptiste Meilhan (Institut Fourier - Université Grenoble Alpes)
Title: When welded knot theory becomes useful for topology
Abstract: Welded knot theory is a combinatorial and diagrammatic extension of classical knot theory. It arises naturally as a quotient of virtual knot theory, introduced in the early 2000s by Kauffman and by Goussarov–Polyak–Viro. The aim of this talk is to present several results showing that welded knot theory turns out to be a relevant and effective tool for topology — not only in knot theory, but also in the study of knotted surfaces in 4-space. This talk assumes no specialized background in topology.
17th of June - Francisco (Kiko) Belchí (La Salle – Universitat Ramon Llull)
Title: Topological Data Analysis of Lung Structure: A Persistent Homology Approach to Chronic Obstructive Pulmonary Disease (COPD)
Abstract: Persistent Homology is a tool from Topological Data Analysis (TDA) that captures the multiscale shape and connectivity structure of data. By examining how topological features (such as connected components, loops, and cavities) persist across scales, it provides a quantitative description of complex geometric patterns that traditional methods often miss. In this talk, I will introduce the core ideas of topology and Persistent Homology with intuitive examples. I will then show how these methods can be applied to medical imaging, focusing on my work on COPD, where Persistent Homology captures structural features that distinguish healthy lungs from those affected by COPD. This illustrates how topological features can become biomarkers in clinical applications.