Applied Algebraic Topology Network Courses

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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• Free Video

Computing Minimal Persistent Cycles - Polynomial and Hard Cases

Explores computing minimal persistent cycles in algebraic topology, discussing polynomial and NP-hard cases, and presenting algorithms for weak pseudomanifolds with applications to scientific data analysis.

• YouTube
• 55 minutes
• Self-Paced
• Free Video

Invariants for Tame Parametrised Chain Complexes

Explore invariants for tame parametrised chain complexes in applied algebraic topology, focusing on explicit constructions, comprehensive frameworks, and discriminative power in topological data analysis.

• YouTube
• 1 hour 3 minutes
• Self-Paced
• Free Video

Wojciech Chachólski - TDA Invariants and Model Categories

Exploring TDA invariants and model categories in data analysis, focusing on simplification techniques from homotopy theory to extract meaningful summaries while balancing information retention.

• YouTube
• 54 minutes
• Self-Paced
• Free Video

Lower Dimensional Topological Information: Theory and Applications

Explore lower dimensional topological features in data analysis, covering detection methods, theoretical foundations, and applications in image segmentation using topological and statistical approaches.

• YouTube
• 51 minutes
• Self-Paced
• Free Video