UConn Math Club
The Kakeya Needle Problem
Vasileios Chousionis (University of Connecticut)
Wednesday, November 8, 2017
In 1917, Kakeya asked for the smallest area of a set in the plane within which a unit line segment (a "needle") can be rotated continuously through 180 degrees, returning to its original position but with reversed orientation. Surprisingly, Besicovitch proved in 1928 that there exist sets of arbitrarily small area within which such a rotation can be achieved! Moreover, he showed that there exist sets with area zero which contain a needle in every direction! One hundred years after Kakeya's question, some of the most famous unsolved problems in analysis involve Kakeya-Besicovitch sets. We are going to describe geometric constructions of Kakeya-Besicovitch sets, touch on their connections to analysis, and discuss their fascinating history.
Comments: Free pizza and drinks!