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Henry Adams - Vietoris-Rips Complexes of Hypercube Graphs

Offered By: Applied Algebraic Topology Network via YouTube

Tags

Vietoris-Rips Complexes Courses Graph Theory Courses Computational Biology Courses Algebraic Topology Courses Homotopy Courses Persistent Homology Courses

Course Description

Overview

Explore the homotopy types of Vietoris-Rips complexes of hypercube graphs at small scale parameters in this 45-minute conference talk. Delve into questions arising from genetic recombination and Kunneth formulas for persistent homology with the sum metric. Learn about the vertex set of hypercube graphs, binary strings, and Hamming distance. Discover how the Vietoris-Rips complex of Q_n changes at different scales, from points to graphs to wedge sums of spheres. Examine the formula for the number of 3-spheres as a function of n and consider open questions about larger scale parameters. Gain insights into homology computations using Ripser++ and explore conjectures based on these findings.

Syllabus

Introduction
VietorisRips complexes
My real motivation
Definitions
Hypercube graphs
Homotopy types
Three ideas
Summary
Thank you
A nice talk
OEIS
Loss of symmetry
Comments


Taught by

Applied Algebraic Topology Network

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