Math Club, February 14^th, 2014.

Maria Alfonseca Cubero

Title: The Kakeya Needle problem

Abstract: What is the area of the smallest set in the plane inside which
a segment of length 1 (the needle) can be rotated 180 degrees?
The surprising solution of this problem is that no matter how small an
area we choose, we can reverse the position of the needle inside a set
of that area. In this talk we will construct such sets and discuss some
of their applications in Analysis.