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Rachel Levanger - A Comparison Framework for Interleaved Persistence Modules

Offered By: Applied Algebraic Topology Network via YouTube

Tags

Algebraic Topology Courses Data Analysis Courses Persistent Homology Courses

Course Description

Overview

Explore a rigorous framework for tracking noise in persistent homology computations in this 1-hour 5-minute talk from the Applied Algebraic Topology Network. Delve into recent advancements that allow for precise monitoring of errors introduced during barcode and persistence diagram calculations. Examine various examples, including sub-sampling and discretization techniques, and compare this approach to traditional uniform error measurements using Bottleneck distance. Discover how this framework addresses an open problem related to non-uniform sub-level set filtrations. Cover topics such as two-dimensional fluid flows, persistent homology, stability, visualization, persistence modules, and digital image analysis.

Syllabus

Introduction
Twodimensional fluid flows
Persistent homology
Stability
Visualization
Persistence modules
Proof sketch
Proof
Discretization
Digital image
Persistence homology


Taught by

Applied Algebraic Topology Network

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