Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Tuesday, July 21, 2015, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Micha Sharir (Tel Aviv University)

A new look at rigidity

We note that the problem of testing for the rigidity of a straight-edge embedding of a graph in the plane can be transformed into a problem involving contacts between lines in three dimensions, using Elekes's transformation (that has been a major component of Guth and Katz's work on distinct distances). This works both ways: By studying the contact patterns of lines in space, we are able to derive new proofs, with stronger characterizations, for the rigidity (or lack thereof) of certain types of graphs (e.g., complete bipartite graphs). On the other hand, results and questions about rigidity translate to interesting properties of lines in space.

Joint work with Orit E. Raz.

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