Luis Scoccola (5/3/21): Approximate and discrete vector bundles скачать в хорошем качестве

Luis Scoccola (5/3/21): Approximate and discrete vector bundles

Synchronization problems, such as the problem of reconstructing a 3D shape from a set of 2D projections, can often be modeled by principal bundles. Similarly, the application of local PCA to a point cloud concentrated around a manifold approximates the tangent bundle of the manifold. In the first case, the characteristic classes of the bundle provide obstructions to global synchronization, while, in the second case, they provide obstructions to dimensionality reduction. This talk was part of the workshop on "Topological Data Analysis - Theory and Applications" supported by the Tutte Institute and Western University: https://math.sci.uwo.ca/~jardine/TDA-...