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Explore the Kakeya set conjecture in three-dimensional space through this mathematical lecture delivered by Hong Wang from IHES and Courant Institute, NYU. Learn about Kakeya sets, which are compact sets in R^n containing a unit line segment pointing in every direction, and examine the conjecture asserting that every Kakeya set has Hausdorff dimension n. Discover the key ideas behind proving the Kakeya set conjecture in R^3, building upon previous results on sticky Kakeya sets developed in collaboration with Josh Zahl. This presentation forms part of the CRM Nirenberg Lectures in Geometric Analysis series, offering insights into advanced geometric analysis and the mathematical techniques used to approach this fundamental problem in harmonic analysis and geometric measure theory.
