As part of the workshop "Geometric Harmonic Analysis in the Discrete and Continuous Settings”, which will take place at the Instituto de Matemáticas de la Universidad de Granada (IMAG) from June 7-13, 2026, we are pleased to announce a public colloquium by Joshua Zahl (Chern Institute of Mathematics at Nankai University).
The lecture will be open to all interested participants.
Title: The Besicovitch compression phenomenon and the Kakeya set conjecture
Date and time: -
Location: IMAG, Main Meeting Room - Calle Rector López Argüeta
Abstract: In 1919, Besicovitch constructed a compact set in the plane with Lebesgue measure 0 that contains a unit line segment pointing in every direction. Such objects are now called measure 0 Besicovitch sets (aka Kakeya sets). By replacing a measure zero Besicovitch set by its delta-thickening, one obtains a collection of 1 x delta rectangles pointing in different directions, the sum of whose areas is 1, but whose union has very small volume. The existence of such collections of rectangles is called the Besicovitch compression phenomenon.
The Kakeya set conjecture is a quantitative statement controlling the strength of the Besicovitch compression phenomenon. In this talk, I will discuss connections between the Besicovitch compression phenomenon, the Kakeya set conjecture, and questions in harmonic analysis and PDE.
We warmly encourage attendance from researchers, students, and anyone interested in harmonic analysis and related areas.
Further information about the workshop can be found through: https://wpd.ugr.es/~imag/birs-imag/