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SUMMARY:Bo'az Klartag (Weizmann Institute)
DTSTART:20200512T143000Z
DTEND:20200512T153000Z
DTSTAMP:20260423T021259Z
UID:OAGAS/9
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OAGAS/9/">Ri
 gidity of Riemannian embeddings of discrete metric spaces</a>\nby Bo'az Kl
 artag (Weizmann Institute) as part of Online asymptotic geometric analysis
  seminar\n\n\nAbstract\nLet M be a complete\, connected Riemannian surface
  and suppose that S is a discrete subset of M. What can we learn about M f
 rom the knowledge of all distances in the surface between pairs of points 
 of S? We prove that if the distances in S correspond to the distances in a
  2-dimensional lattice\, or more generally in an arbitrary net in R^2\, th
 en M is isometric to the Euclidean plane. We thus find that Riemannian emb
 eddings of certain discrete metric spaces are rather rigid. A corollary is
  that a subset of Z^3 that strictly contains a two-dimensional lattice can
 not be isometrically embedded in any complete Riemannian surface. This is 
 a joint work with M. Eilat.\n
LOCATION:https://researchseminars.org/talk/OAGAS/9/
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