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Explore the fascinating world of algebraic topology applied to graphs and mesoscopic spaces in this insightful lecture. Delve into the concept of mesoscopic spaces, defined as metric spaces with a privileged scale, and discover recent developments in their algebraic topology. Learn how mesoscopic spaces, reflexive graphs, and topological spaces naturally induce pseudotopological spaces, particularly Cech closure spaces. Examine methods for studying homotopy and homology in these categories. Investigate the adaptation of this perspective to semi-uniform spaces, leading to the construction of a version of Hausmann's metric cohomology at arbitrary scales. Gain understanding of how this approach enables the proof of results on homotopy invariance and excision for Vietoris-Rips (co)homology. Enhance your knowledge of advanced mathematical concepts and their applications in this 54-minute presentation by Antonio Rieser, delivered for the Applied Algebraic Topology Network.
