Comments on: Open question: best bounds for cap sets
https://terrytao.wordpress.com/2007/02/23/open-question-best-bounds-for-cap-sets/
Updates on my research and expository papers, discussion of open problems, and other maths-related topics. By Terence TaoWed, 08 Jul 2020 16:00:52 +0000
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By: To cheer you up in difficult times 7: Bloom and Sisask just broke the logarithm barrier for Roth’s theorem! | Combinatorics and more
https://terrytao.wordpress.com/2007/02/23/open-question-best-bounds-for-cap-sets/#comment-572661
Wed, 08 Jul 2020 16:00:52 +0000http://terrytao.wordpress.com/2007/02/23/open-question-best-bounds-for-cap-sets/#comment-572661[…] related problem in . It is called the cap set problem. A subset of is called a cap set if it contains no arithmetic progression of size three or, […]
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By: The Geometry of SET | Infinite Series | Wordpress Tutorials
https://terrytao.wordpress.com/2007/02/23/open-question-best-bounds-for-cap-sets/#comment-508531
Sat, 08 Dec 2018 21:18:21 +0000http://terrytao.wordpress.com/2007/02/23/open-question-best-bounds-for-cap-sets/#comment-508531[…] Open Question: Best Bounds for Cap Sets (blog post by Terry Tao) Open question: best bounds for cap sets […]
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By: The Mathematical Beauty of the Game SET | The Aperiodical
https://terrytao.wordpress.com/2007/02/23/open-question-best-bounds-for-cap-sets/#comment-503308
Sun, 22 Jul 2018 10:00:50 +0000http://terrytao.wordpress.com/2007/02/23/open-question-best-bounds-for-cap-sets/#comment-503308[…] rich mathematics embedded in SET, perhaps fields medalist Terry Tao can convince you otherwise. In his blog in 2007, he wrote, “Perhaps my favourite open question is the problem on the maximal size of […]
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By: The Geometry of SET | Infinite Series | Raket Science
https://terrytao.wordpress.com/2007/02/23/open-question-best-bounds-for-cap-sets/#comment-494862
Wed, 28 Mar 2018 00:10:26 +0000http://terrytao.wordpress.com/2007/02/23/open-question-best-bounds-for-cap-sets/#comment-494862[…] Open question: best bounds for cap sets […]
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By: Introduction to the polynomial method (and other similar things) | Short, Fat Matrices
https://terrytao.wordpress.com/2007/02/23/open-question-best-bounds-for-cap-sets/#comment-472235
Fri, 09 Sep 2016 17:48:53 +0000http://terrytao.wordpress.com/2007/02/23/open-question-best-bounds-for-cap-sets/#comment-472235[…] The obvious bounds on are and , and with a bit of extra work, these were improved to and . On his blog, Terry Tao suspected that the lower bound could be improved all the way up to , and in one of his […]
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By: A symmetric formulation of the Croot-Lev-Pach-Ellenberg-Gijswijt capset bound | What's new
https://terrytao.wordpress.com/2007/02/23/open-question-best-bounds-for-cap-sets/#comment-468721
Wed, 18 May 2016 08:13:26 +0000http://terrytao.wordpress.com/2007/02/23/open-question-best-bounds-for-cap-sets/#comment-468721[…] that does not contain any lines. A basic problem in additive combinatorics (discussed in one of the very first posts on this blog) is to obtain good upper and lower bounds for the maximal size of a capset in […]
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By: The new bound on cap sets | Anurag's Math Blog
https://terrytao.wordpress.com/2007/02/23/open-question-best-bounds-for-cap-sets/#comment-468701
Tue, 17 May 2016 22:50:43 +0000http://terrytao.wordpress.com/2007/02/23/open-question-best-bounds-for-cap-sets/#comment-468701[…] problem in combinatorics that survived even after a lot of effort from several mathematicians (see this, this, this and this). Ultimately, just like the finite field Kakeya problem, it succumbed to the […]
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By: kodlu
https://terrytao.wordpress.com/2007/02/23/open-question-best-bounds-for-cap-sets/#comment-468678
Mon, 16 May 2016 22:00:59 +0000http://terrytao.wordpress.com/2007/02/23/open-question-best-bounds-for-cap-sets/#comment-468678I found your response to Greg Kuperberg illuminating. Also, the counterexample in the last paragraph of the post may have a typo; shouldn’t it be $\{0,1\}^m \times F_3^n$?

[Corrected, thanks – T.]

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By: Mind Boggling: Following the work of Croot, Lev, and Pach, Jordan Ellenberg settled the cap set problem! | Combinatorics and more
https://terrytao.wordpress.com/2007/02/23/open-question-best-bounds-for-cap-sets/#comment-468636
Sun, 15 May 2016 13:20:48 +0000http://terrytao.wordpress.com/2007/02/23/open-question-best-bounds-for-cap-sets/#comment-468636[…] is amazing! The cap set problem was quite popular here on the blog, see also Tao’s 2007 post, and Jordan made also quite an effort over the years in proving the other direction before proving […]
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By: Terence Tao
https://terrytao.wordpress.com/2007/02/23/open-question-best-bounds-for-cap-sets/#comment-468583
Fri, 13 May 2016 22:52:29 +0000http://terrytao.wordpress.com/2007/02/23/open-question-best-bounds-for-cap-sets/#comment-468583So, the solution to this problem actually took nine years, rather than a week, but anyway: Jordan Ellenberg has just shown that capsets are asymptotically bounded in size by .
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