An Introduction to Persistent Homology

Explore the fundamentals of applied and computational topology in this 55-minute webinar, focusing on persistent homology and its applications to energy landscapes in chemistry. Gain a visual understanding of topology and homology groups, and delve into sublevelset persistent homology for summarizing real-valued functions, particularly energy functions. Discover how persistent homology can be applied to point cloud data, potentially sampled from low-energy conformations in chemical systems. Cover key topics including sublevel sets, digital ecology, scanning error, stability theorem, and the intersection of persistent homology with machine learning. Enhance your understanding of topological data analysis and its practical applications in scientific research.

Introduction
Persistent homology
Sublevel sets
Explanation
Grid
Digital ecology
Scanning error
Stability theorem
Pointcloud persistence
Machine Learning
Summary