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Waists measured via Urysohn width

By Alexey Balitsky

The Urysohn width measures the "approximate dimension" of a riemannian manifold by approximating it with a lower-dimensional simplicial complex. Positive scalar curvature conjecturally implies upper bounds on the width. An inductive approach to this conjecture and related ones requires understanding of the following question: If our manifold is sliced into chunks of small approximate dimension, does that imply that the manifold itself has controlled approximate dimension? I will explain a few results in that direction, mostly of negative nature.

Information about the video

  • Date of recording 22/05/2024
  • Date of publication 03/06/2024
  • Institution IHES
  • Language English
  • Audience Researchers
  • Format MP4

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