Applied Algebraic Topology Network Courses

Morse-Based Fibering of the Rank Invariant

Explore multi-parameter persistence in data analysis using discrete Morse theory to compute rank invariants, partition parameter space, and deduce persistence diagrams for equivalent classes of lines.

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

Sheaves as Computable and Stable Topological Invariants for Datasets

Explores sheaf theory in topological data analysis, connecting level-sets persistence with derived sheaves. Presents functorial equivalences, stability theorems, and barcode decompositions for continuous data analysis.

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

Epsilon-Net Induced Lazy Witness Complex for Topological Data Analysis

Efficient topological data analysis using epsilon-net induced lazy witness complex. Improves scalability and approximation in persistent homology computation with theoretical guarantees and algorithmic implementations.

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

TALLEM - Topological Assembly of Locally Linear Euclidean Models

Explore a novel topological data analysis tool for nonlinear dimensionality reduction, assembling local Euclidean coordinates to create globally consistent maps that respect data topology.

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

Embeddings and Tverberg-Type Problems: New Algorithms and Undecidability Results

Explore computational topology: algorithmic embeddability, undecidability in higher dimensions, and polynomial-time decidability of r-Tverberg problem in metastable range.

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

Counting Embedded Spheres with the Same Persistence

Explores inverse problems in Topological Data Analysis, providing a formula for unbraided height equivalence classes of embedded two-spheres with prescribed level-set barcodes from z-axis projection.

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

Topological Data Analysis for Quantifying Plant Morphology

Explore topological data analysis for plant morphology using persistent homology and Euclidean Distance Transform. Learn applications in hurricane video data and XRay CT scans of plants.

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

Topological Data Analysis to Detect Fake Faces From Images and Videos

Explore topological data analysis for detecting fake faces in images and videos. Learn about image landmarks, texture descriptors, and performance testing on passport photos and DeepFake videos.

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

Topological Analysis of Convolutional Neural Network Layers for Image Analysis

Explore the impact of CNN layers on image topological texture features, examining their effectiveness in detecting subtle changes and understanding decision-making processes in image analysis.

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

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

Peter Bubenik - Topological Data Analysis for Biological Images

Explore topological data analysis for biological images, combining persistent homology with machine learning to classify cell structures and analyze various image types.

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

Convex Sunflower Theorems and Neural Codes

Explore convex sunflower theorems and neural codes, connecting neuroscience with discrete geometry to understand place cell encoding and cognitive mapping in rat hippocampus.

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

Stable and Consistent Density-Based Clustering

Explore stable and consistent density-based clustering methods, including a novel 3-parameter hierarchical approach. Learn about stability theorems and their applications in various clustering algorithms.

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

Borsuk-Ulam Theorems into Higher-Dimensional Codomains

Exploration of Borsuk-Ulam theorems in higher dimensions, generalizing results and discussing open questions related to optimal diameters and Schur polynomials.

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

An Introduction to the Topology ToolKit

Comprehensive introduction to the Topology ToolKit (TTK) for topological data analysis and visualization, covering usage in ParaView and Python, advanced features, and resources for further learning.

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