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Explore the mathematical concept of sticky Kakeya sets in this lecture from the CRM Nirenberg Lectures in Geometric Analysis series. Learn about this special class of Kakeya sets that exhibit approximate self-similarity at every location and scale, and discover the sticky Kakeya conjecture which asserts that every sticky Kakeya set in R^n has Hausdorff dimension n. Examine the historical progress on the Kakeya conjecture over several decades and understand how the 2022 proof of the sticky Kakeya conjecture in dimension 3 by Joshua Zahl and Hong Wang became a crucial component in their subsequent proof of the Kakeya set conjecture in dimension 3. Gain insights into this significant breakthrough in geometric analysis through a presentation designed for a general mathematical audience, featuring joint research work with Hong Wang from Nankai University.
