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

Introduction to Algebraic Topology (Part-I)
Indian Institute of Technology Bombay via Swayam Introduction to Algebraic Topology (Part-II)
NPTEL via Swayam Intro to the Fundamental Group - Algebraic Topology with Tom Rocks Maths
Dr Trefor Bazett via YouTube Neural Sense Relations and Consciousness - A Diagrammatic Approach
Models of Consciousness Conferences via YouTube Classification of 2-Manifolds and Euler Characteristic - Differential Geometry
Insights into Mathematics via YouTube