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SUMMARY:Luis Scoccola (Michigan State University)
DTSTART:20210419T123000Z
DTEND:20210419T133000Z
DTSTAMP:20260422T135734Z
UID:BilTop/20
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/BilTop/20/">
 Approximate and discrete vector bundles in theory and applications</a>\nby
  Luis Scoccola (Michigan State University) as part of Bilkent Topology Sem
 inar\n\nLecture held in SB-Z11.\n\nAbstract\nSynchronization problems\, su
 ch as the problem of reconstructing a 3D shape from a set of 2D projection
 s\, 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 characteristi
 c classes of the bundle provide obstructions to global synchronization\, w
 hile\, in the second case\, they provide topological information of the ma
 nifold beyond its homology\, and give obstructions to dimensionality reduc
 tion. I will describe joint work with Jose Perea in which we propose notio
 ns of approximate and discrete vector bundle\, study the extent to which t
 hey determine true vector bundles\, and give algorithms for the stable and
  consistent computation of low-dimensional characteristic classes directly
  from these combinatorial representations.\n
LOCATION:https://researchseminars.org/talk/BilTop/20/
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