YoVDO

Saecular Persistence

Offered By: Applied Algebraic Topology Network via YouTube

Tags

Algebraic Topology Courses Functors Courses Topological Data Analysis Courses Persistence Modules Courses

Course Description

Overview

Explore the concept of saecular persistence in this comprehensive lecture from the Applied Algebraic Topology Network. Delve into a categorically natural method for decomposing persistence modules with non-field coefficients into families of interval modules. Examine how this approach generalizes existing factorizations of 1-parameter persistence modules, leading to persistence diagrams in both homology and homotopy. Discover applications of saecular decomposition, including inverse and extension problems involving filtered topological spaces, generalized persistence diagrams, and the Leray-Serre spectral sequence. Learn about key tools such as modular, semimodular, and distributive order lattices, as well as RE/Puppe exact categories. Gain insights into how this approach extends beyond field coefficients to integer coefficients and homotopy, offering a broader perspective on topological data analysis.

Syllabus

Gregory Henselman-Petrusek (9/28/22): Saecular persistence


Taught by

Applied Algebraic Topology Network

Related Courses

Topological Data Analysis - New Perspectives on Machine Learning - by Jesse Johnson
Open Data Science via YouTube
Analyzing Point Processes Using Topological Data Analysis
Applied Algebraic Topology Network via YouTube
MD Simulations and Machine Learning to Quantify Interfacial Hydrophobicity
Applied Algebraic Topology Network via YouTube
Topological Data Analysis of Plant-Pollinator Resource Complexes - Melinda Kleczynski
Applied Algebraic Topology Network via YouTube
Hubert Wagner - Topological Data Analysis in Non-Euclidean Spaces
Applied Algebraic Topology Network via YouTube