Coursera Spring Sale
40% Off Coursera Plus Annual!
Grab it
Explore the fascinating world of geometric analysis through this mathematical lecture that delves into the Besicovitch compression phenomenon and its connection to the famous Kakeya set conjecture. Learn about Besicovitch's groundbreaking 1919 construction of a compact set in the plane with zero Lebesgue measure that remarkably contains a unit line segment pointing in every direction. Discover how these measure zero Besicovitch sets, also known as Kakeya sets, lead to the intriguing compression phenomenon where collections of rectangles with total area 1 can have unions of arbitrarily small volume. Understand the quantitative nature of the Kakeya set conjecture as it attempts to control the strength of this compression phenomenon. Examine the deep connections between these geometric concepts and their applications in harmonic analysis and partial differential equations. This presentation, part of the CRM Nirenberg Lectures in Geometric Analysis series, is designed for a general mathematical audience and provides insight into one of the most compelling problems in modern geometric analysis.
