Approximate and Discrete Vector Bundles

Explore the concept of approximate and discrete vector bundles in this one-hour lecture by Luis Scoccola, presented as part of the Applied Algebraic Topology Network. Delve into the world of synchronization problems, such as reconstructing 3D shapes from 2D projections, and learn how these can be modeled using principal bundles. Discover the application of local PCA to point clouds concentrated around manifolds and how it approximates the tangent bundle. Understand the significance of characteristic classes in providing obstructions to global synchronization and dimensionality reduction. Gain insights into the intersection of topology and data analysis, as presented in the workshop on "Topological Data Analysis - Theory and Applications" supported by the Tutte Institute and Western University.