YoVDO

Antonio Rieser - Algebraic Topology for Graphs and Mesoscopic Spaces

Offered By: Applied Algebraic Topology Network via YouTube

Tags

Algebraic Topology Courses Topological Spaces Courses Homotopy Courses Homologies Courses

Course Description

Overview

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.

Syllabus

Antonio Rieser (03/29/23): Algebraic Topology for Graphs and Mesoscopic Spaces


Taught by

Applied Algebraic Topology Network

Related Courses

Introduction to Algebraic Topology (Part-II)
NPTEL via Swayam
Computing Optimal Homotopies
Applied Algebraic Topology Network via YouTube
Henry Adams - Vietoris-Rips Complexes of Hypercube Graphs
Applied Algebraic Topology Network via YouTube
Mikhail Katz - Collapsing Surfaces
Applied Algebraic Topology Network via YouTube
Data Complexes, Obstructions, Persistent Data Merging
Applied Algebraic Topology Network via YouTube