Title: What is the Kakeya Needle Problem?
Speaker: Daniel Glasscock (OSU)
Abstract: The following famous problem originated in the work of Japanese mathematician Soichi Kakeya in 1917: What is the planar figure of least area in which a unit line segment may be turned through 360 degrees by a continuous movement? A circle of diameter 1 is clearly such a figure; can you find a figure with lesser area?
Around the same time, Russian mathematician Abram Besicovitch solved a "twin" problem originating from analysis: there exists a planar set of zero area containing a line segment in every direction. Besicovitch hadn't yet heard of Kakeya's problem, and no one outside of isolated Russia had heard of Besicovitch's result. Four years later, after emigrating to Europe, Besicovitch was introduced to the Kakeya problem and had the tools to solve it. His counter-intuitive solution may surprise you!
In this talk, I'll go through this history in more detail, outline Besicovitch's ingenious solution to the Kakeya problem, and, time permitting, explain how the Kakeya problem sits at the intersection of modern research in several different fields.