Applied Algebraic Topology Network Courses

Bala Krishnamoorthy: Linear Programming in Geometric Measure Theory

Explore geometric measure theory through linear programming, examining integral currents, simplicial flat norm, and polyhedral approximation. Discover applications in median shape analysis.

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

Benjamin Schweinhart - Statistical Topology of Random Cell Complexes, and Applications

Explore statistical topology of random cell complexes, covering curvature flow, grain growth, graph limits, and computational evidence for steady state hypothesis.

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

Greg Malen - Collapsibility of Random Clique Complexes

Explore k-collapsibility in random clique complexes, examining dimensional faces, strong connectivity, and homology implications for topological data analysis.

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

Category Weight Estimates of Minimal Triangulations

Explore LS-category methods for estimating minimal triangulations of manifolds and polyhedra, focusing on lower bounds for vertex counts in space triangulations.

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

Decomposing Simplicial Complexes - Without Losing Pieces

Explore simplicial complex decomposition, its impact on homotopy type, and applications in Vietoris-Rips complexes. Learn about obstruction complexes and their role in understanding topological changes.

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

Tropical Geometry of Phylogenetic Tree Spaces

Explore tropical geometry's application to phylogenetic tree spaces, examining BHV space, tropical Grassmannians, and their implications for computational biology and statistics.

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

Intrinsic Topological Transforms via the Distance Kernel Embedding

Explore topological transforms for abstract metric spaces using distance kernel embedding, combining persistent homology with Euclidean embeddings for enhanced shape analysis and discrimination.

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

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

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
• On-Demand
• 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
• On-Demand
• Free Video

Oliver Vipond - Local Equivalence of Metrics for Multiparameter Persistence Modules

Explore local equivalence of metrics for multiparameter persistence modules, focusing on fibered bar codes' discriminative power and stability in topological data analysis.

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

Topology in Chemistry Applications

Explore topological data analysis in chemistry, focusing on molecular relationships, graph theory, and network analysis to extract new insights from chemical data.

• YouTube
• 1 hour 7 minutes
• On-Demand
• Free Video

Catastrophe Theory

Explore catastrophe theory, covering critical points, germs, classification theorems, unfoldings, and elementary catastrophes. Visualize concepts and discover applications in chemistry.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

TDALabs - Some of TDA's Greatest Hits in Interactive Python

Interactive exploration of TDA's key applications using Python, covering time series analysis, image processing, 3D shape clustering, and more. Hands-on examples showcase TDA's versatility and practical uses.

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

Henry Adams and Enrique Alvarado - An Introduction to Morse Theory

Explore Morse theory's applications in topology, including CW complexes, key theorems, and simplification techniques, with real-world examples in material science.

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