Speaker: 王虹教授，纽约大学

Inviter: 数学所

Title: Kakeya sets in R^3

Language: Chinese

Time & Venue: 2025.06.25 10:30-11:30 数学院南楼N204

Abstract: In 1917, Soichi Kakeya asked what is the minimum area of a region in which a needle of unit length can be turned through 360 degrees. Surprisingly, Besicovitch provided in 1919 an example that the area could be arbitrarily small! But how small could it be? This question leads to the study of the Kakeya sets, a subject in the intersection of geometric measure theory and Fourier analysis. A Kakeya set in the n-dimensional Euclidean space is a bounded subset that contains a unit line segment pointing in every direction. Kakeya set conjecture asserts that every Kakeya set has Hausdorff dimension n. We prove this conjecture in three dimensional space as a consequence of a more general statement about union of tubes. This is joint work with Zahl.