# Seminars & Colloquia Calendar

## Approximate and Discrete Vector Bundles in Theory and Applications

#### Luis Scoccola, Michigan State University

Location: ** Zoom**

Date & time: Friday, 16 April 2021 at 2:00PM - 3:00PM

*Abstract: 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 topological* *information of the manifold beyond its homology, and in particular, give 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.*

Meeting ID: 464 647 321

Passcode: 061956

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