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  "cid": "bafyreif2fsef3wpyam2u7op5txekzxxpl37pn6fkrcllefmjqenpcen6iu",
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    "text": "I am happy to announce that the Kakeya set conjecture, one of the most sought after open problems in geometric measure theory, has now been proven (in three dimensions) by Hong Wang and Joshua Zahl! arxiv.org/abs/2502.17655  I discuss some ideas of the proof at terrytao.wordpress.com/2025/02/25/t...",
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        "title": "Volume estimates for unions of convex sets, and the Kakeya set conjecture in three dimensions",
        "description": "We study sets of $δ$ tubes in $\\mathbb{R}^3$, with the property that not too many tubes can be contained inside a common convex set $V$. We show that the union of tubes from such a set must have almos..."
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            "uri": "https://terrytao.wordpress.com/2025/02/25/the-three-dimensional-kakeya-conjecture-after-wang-and-zahl/",
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    "createdAt": "2025-02-26T04:49:17.720Z"
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