Come join us at 6pm on Wednesday, July 18, when Professor Peter Winkler will be giving a Math Society Talk in Kemeny 108.  Pizza and soft drinks will be provided.

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  A Cop and Robber Solve the Kakeya Needle Problem

                       Professor Peter Winkler (Mathematics/Computer Science)

July 18, 6pm, Kemeny 108

    In 1917 Soichi Kakeya asked for the least-area region of the plane in which a
unit-length needle could be rotated 180 degrees; in 1925, Avram Besicovitch
famously showed that there were arbitrarily small regions with this property.  In
joint work with Y. Babichenko, Y. Peres, Y. Peretz and P. Sousi (2012), we show
that simply by following optimal strategies in a certain pursuit-and-evasion game,
the players construct a Kakeya set which is in some sense the best solution known.

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Illustration of an example Kakeya needle set: http://i.imgur.com/5aUzD.gif