Speaker: Nets Hawk Katz
Title: The Kakeya problem and semialgebraic sets
Abstract: One of the most important outstanding questions in analysis today is the Kakeya problem. The goal is to show that a compact set in Rn containing a unit line segment in every direction must have full Hausdorff dimension. We discuss the history and motivations of the problem, and the direction of recent research on it. One of the remarkable things about the problem is the number of different areas of mathematics from which tools have been successfully used. We end with a recent application of the tools of real algebraic geometry.