Approximate vector bundles and fiberwise dimensionality reduction

I will describe joint work with Jose Perea in which we propose combinatorial notions of vector bundle, study the extent to which these determine true vector bundles, and give algorithms for the stable and consistent computation of low-dimensional characteristic classes directly from these representations. I will also show how this framework can be used to frame a dimensionality reduction algorithm which preserves the global topology as well as the local linear structure of data.

This talk will be hybrid, held in-person and online on Zoom