Applied Algebraic Topology Network Courses

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

Graph Representation Learning and Its Applications to Biomedicine

Graph representation learning techniques for biomedical applications, focusing on SubGNN for disentangled subgraph embeddings and their use in predicting disease treatments and safe drug combinations.

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

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
• Self-Paced
• Free Video

Topological Complexity of Pure Graph Braid Groups

Explore topological complexity in graph braid groups, focusing on Farber's conjecture about ordered configuration spaces and its implications for topological robotics.

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

Nonlinear Dynamics in an Age of Heuristic Science

Explore nonlinear dynamics through combinatorial topology, offering efficient computational methods and new perspectives for multiscale systems and data-driven science in biology and engineering.

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

Luis Scoccola - Locally Persistent Categories & Metric Properties of Interleaving Distances

Explore locally persistent categories, metric properties of interleaving distances, and their applications in algebraic topology, including natural interleavings and weak equivalences.

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