Dear All,

This is an announcement for a Zoom talk by Bo’az Klartag on the subject of Rigidity of Riemannian embeddings of discrete metric spaces, on Tuesday May 12 at 10:30 am EDT. The talk is a part of the online series in asymptotic geometric analysis. All are welcome to attend! Info below.

Link for Zoom: https://zoom.us/j/690046404

Website: http://people.math.gatech.edu/~glivshyts6/AGAonline.html

Tuesday, May 12, 10:30 am (New York, NY time)

Bo'az Klartag, Weizmann Institute, Rehovot, Israel

Topic: Rigidity of Riemannian embeddings of discrete metric spaces

Abstract: Let M be a complete, connected Riemannian surface and suppose that S is a discrete subset of M. What can we learn about M from 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, then M is isometric to the Euclidean plane. We thus find that Riemannian embeddings of certain discrete metric spaces are rather rigid. A corollary is that a subset of Z^3 that strictly contains a two-dimensional lattice cannot be isometrically embedded in any complete Riemannian surface. This is a joint work with M. Eilat.

Sincerely,

The seminar organizers

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