Applied Algebraic Topology Network Courses

Star Clusters in Clique Complexes and the Vietoris-Rips Complex of Planar Sets

Explore star clusters in simplicial complexes and their applications to independence complexes and Vietoris-Rips complexes of planar sets, with insights on homotopy information and related conjectures.

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

Tverberg’s Theorem for Cell Complexes

Explore Tverberg's theorem generalization, homotopy decomposition of discretized configuration spaces, and topological extensions in this advanced algebraic topology discussion.

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

Effectual Topological Complexity

Explora la Complejidad Topológica Efectual, una nueva versión para G-Espacios. Aprende sus propiedades, relación con TC estándar y aplicación en superficies, especialmente en el toro.

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

Mason Porter - Topological Data Analysis of Spatial Complex Systems

Explore topological data analysis in spatial systems, from spider webs to COVID-19 spread. Learn filtered simplicial complexes and their applications in various real-world scenarios.

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

Mikhail Katz - Collapsing Surfaces

Exploring surface collapse in Riemannian geometry, focusing on critical points, intersection theory, and Toponogov comparison. Analyzes fiber homotopy and discrete integration against Euler characteristic.

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

Nerve Theorems for Fixed Points of Neural Networks

Explore how network connectivity shapes neural activity using combinatorial threshold-linear networks. Learn about nerve theorems and their application in understanding fixed points of large neural networks.

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

Topological Complexity Using Arbitrary Covers

Explore topological complexity using arbitrary covers, focusing on sectional category, ANRs, and generalized concepts. Gain insights into advanced algebraic topology techniques and applications.

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

Using Algebraic Geometry to Detect Robustness in Reaction Networks

Explore algebraic geometry techniques to detect robustness in reaction networks, focusing on absolute concentration robustness and its implications for biological systems.

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

Gunnar Carlsson: Topological Deep Learning

Explore topological data analysis in deep learning, reducing data needs and enhancing transparency. Focuses on image and video analysis, network architectures, and applications in various fields.

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

Data Complexes, Obstructions, Persistent Data Merging

Explore data complexes, topological obstructions in database JOIN operations, and persistence levels in data alignment. Learn about measure theory, homotopy, and homology in the context of data integration.

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

Robert Ghrist - Laplacians and Network Sheaves

Explore cellular sheaves, Laplacians, and their applications in social networks and opinion dynamics. Learn about decentralized methods for computing sheaf cohomology and analyzing consensus and polarization.

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

The Gromov-Hausdorff Distance Between Spheres

Explore the Gromov-Hausdorff distance between spheres, its applications in geometry and topology, and methods for calculating precise values between specific sphere pairs.

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

Yulia Gel - Topological Clustering of Multilayer Networks

Explore topological clustering of multilayer networks, focusing on higher-order interactions and local neighborhood shapes. Learn applications in climate-insurance and COVID-19 data analysis.

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

Musing About Robotic Football

Explore robotic football strategies, discussing modeling, non-fibrations, speed, sensing, and topological complexity in the context of navigating blockers to score.

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

How Optimal Transport Can Help Us to Determine Curvature of Complex Networks

Explore Ollivier Ricci curvature in complex networks, its applications in network analysis, and implementation in chemical reaction networks using optimal transport theory.

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