Event Type:

Geometry-Topology Seminar

Date/Time:

Monday, November 8, 2021 - 12:00 to 12:50

Location:

Kidd 280 or contact Christine Escher for a zoom link.

Guest Speaker:

Institution:

Northeastern University

Abstract:

Synchronization problems, such as the problem of reconstructing a 3D shape from a set of 2D projections, can often be modelled by principal bundles, which can be approximated from the input data of the problem. Similarly, by locally approximating a point cloud concentrated around a manifold by linear subspaces (local PCA) one can approximate the tangent bundle of the manifold. In the first case, the characteristic classes of the bundle provide obstructions to synchronization, while, in the second case, they provide obstructions to dimensionality reduction. I will describe joint work with Jose Perea in which we propose several notions of approximate and discrete vector bundle, study the extent to which they determine true vector bundles, and give algorithms for the stable and consistent computation of low-dimensional characteristic classes directly from these combinatorial representations. No previous knowledge of the theory of vector bundles will be assumed.

Host: