Persistent Homology Courses and Certifications

Applied Algebraic Topology Network

An Introduction to Persistent Homology

Explore persistent homology in applied topology, focusing on energy landscapes in chemistry. Learn about sublevelset analysis and its applications to real-valued functions and point cloud data.

• YouTube
• 55 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

Computing Persistent Homology - Introduction

Explore the fundamentals of persistent homology computation, covering key concepts, intuition, and practical applications in topological data analysis.

• YouTube
• 27 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

From Persistent Homology to Machine Learning

Overview of persistent homology's applications in machine learning, exploring its use in analyzing global topology and local geometry of datasets, with examples from various fields and discussions on stability and interpretability.

• YouTube
• 29 minutes
• On-Demand
• Free Video

Institute for Advanced Study

Studying Fluid Flows with Persistent Homology - Rachel Levanger

Explore fluid dynamics through persistent homology, uncovering patterns in complex systems like turbulence and convection. Learn topological data analysis techniques for studying fluid flows.

• YouTube
• 57 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

Liquid Crystals Dynamics - What Persistent Homology Reveals

Explore liquid crystal phase transitions through persistent homology, revealing thermodynamic features and structural changes in nanocomposites using advanced data analysis techniques.

• YouTube
• 57 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

Detecting Bifurcations in Dynamical Systems with Zigzag Persistent Homology

Explore zigzag persistent homology for efficient detection of bifurcations in dynamical systems, reducing computational costs and capturing topological changes in a single persistence diagram.

• YouTube
• 24 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

Generalized Morse Theory of Distance Functions to Surfaces for Persistent Homology

Unifying distance fields, persistent homology, and Morse theory to quantify complex shape textures, with applications in characterizing vascular structures in leukemia samples.

• YouTube
• 44 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

Minimal Cycle Representatives in Persistent Homology Using Linear Programming

Explores optimization techniques for selecting minimal cycle representatives in persistent homology, comparing effectiveness and computational costs of various algorithms using linear programming methods.

• YouTube
• 50 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

Non-Diffusive Vortexes at Transition State of Activated Process by Persistent Homology

Exploring non-diffusive dynamics in molecular transitions using persistent homology, revealing reactive vortexes and rotational fluxes at transition states of alanine-dipeptide isomerization.

• YouTube
• 33 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

Ippei Obayashi - Stable Volumes for Persistent Homology

Explore stable volumes in persistent homology: a novel method to identify robust topological structures in data, overcoming instability issues and revealing minimal building blocks.

• YouTube
• 54 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

Stability of 2-Parameter Persistent Homology

Explores stability results for 2-parameter persistent homology, covering multicover bifiltration, subdivision bifiltrations, and degree bifiltrations. Discusses computational aspects and implications for practical applications.

• YouTube
• 55 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

Don Sheehy - Persistent Homology of Lipschitz Extensions

Explore persistent homology of Lipschitz functions, analyzing sublevel set filtrations and barcodes from sample data. Learn about sub-barcodes and their theoretical guarantees in topological data analysis.

• YouTube
• 1 hour 5 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

Geometric Approaches on Persistent Homology

Explore geometric interpretations of persistence diagrams, focusing on quantitative descriptions of homology class size and persistence, with analysis of power filtration on unweighted graphs.

• YouTube
• 1 hour 9 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

Vietoris-Rips Persistent Homology, Injective Metric Spaces, and The Filling Radius

Explore geometric persistent homology, its isomorphism with Vietoris-Rips filtration, and applications in characterizing persistence barcodes, bounding intervals, and connecting to filling radius.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

Multiple Hypothesis Testing with Persistent Homology

Exploring methods for multiple hypothesis testing in persistent homology, including family-wise error rates and false discovery rates, with applications to Mapper complex validation.

• YouTube
• 57 minutes
• On-Demand
• Free Video