Sticky Kakeya Sets and the Sticky Kakeya Conjecture

Explore the intricacies of Kakeya sets and the sticky Kakeya conjecture in this hour-long lecture by Joshua Zahl from the University of British Columbia. Delve into the world of compact subsets of R^n containing unit line segments pointing in every direction, and examine the Kakeya conjecture's assertion that these sets must have dimension n. Discover the connections between this conjecture and open problems in harmonic analysis, as well as its significance in understanding the behavior of the Fourier transform in Euclidean space. Learn about sticky Kakeya sets, a special class exhibiting approximate self-similarity at multiple scales, and their role in Katz, Łaba, and Tao's groundbreaking 1999 work. Investigate the specific case of the Kakeya conjecture related to sticky Kakeya sets, and gain insights into the proof of this conjecture in dimension 3, based on joint work with Hong Wang. This lecture, part of the Colloque des sciences mathématiques du Québec, offers a deep dive into advanced mathematical concepts for those interested in geometric measure theory and harmonic analysis.