YoVDO

A Counter-Example to Hausmann's Conjecture

Offered By: Applied Algebraic Topology Network via YouTube

Tags

Algebraic Topology Courses Mathematical Proofs Courses Topological Spaces Courses Persistent Homology Courses Homotopy Theory Courses Vietoris-Rips Complexes Courses

Course Description

Overview

Explore a groundbreaking lecture that challenges a long-standing conjecture in algebraic topology. Delve into the world of Vietoris-Rips complexes and their connectivity as Žiga Virk presents a counter-example to Hausmann's conjecture from 1995. Learn about the stability property of persistent homology and its crucial role in disproving the monotonicity of Vietoris-Rips complex connectivity. Gain insights into the implications of this discovery for closed compact Riemannian manifolds and their homotopy equivalence to Vietoris-Rips complexes at small scale parameters.

Syllabus

Žiga Virk (4/24/21): A counter-example to Hausmann's conjecture


Taught by

Applied Algebraic Topology Network

Related Courses

Lie Algebras and Homotopy Theory - Jacob Lurie
Institute for Advanced Study via YouTube
Univalence from a Computer Science Point-of-View - Dan Licata
Institute for Advanced Study via YouTube
Artin Reciprocity via Spheres
Fields Institute via YouTube
Basic Homotopy Theory by Samik Basu
International Centre for Theoretical Sciences via YouTube
Star Clusters in Clique Complexes and the Vietoris-Rips Complex of Planar Sets
Applied Algebraic Topology Network via YouTube