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Monthly Archives: May 2016
Polymath 10 post 6: The Erdos-Rado sunflower conjecture, and the Turan (4,3) problem: homological approaches.
In earlier posts I proposed a homological approach to the Erdos-Rado sunflower conjecture. I will describe again this approach in the second part of this post. Of course, discussion of other avenues for the study of the conjecture are welcome. The purpose … Continue reading
Polymath 10 Emergency Post 5: The Erdos-Szemeredi Sunflower Conjecture is Now Proven.
While slowly writing Post 5 (now planned to be Post 6) of our polymath10 project on the Erdos-Rado sunflower conjecture, the very recent proof (see this post) that cap sets have exponentially small density has changed matters greatly! It implies … Continue reading
Mind Boggling: Following the work of Croot, Lev, and Pach, Jordan Ellenberg settled the cap set problem!
A quote from a recent post from Jordan Ellenberg‘s blog Quomodocumque: Briefly: it seems to me that the idea of the Croot-Lev-Pach paper I posted about yesterday (GK: see also my last post) can indeed be used to give a new bound … Continue reading
Posted in Combinatorics, Open problems, Updates
Tagged Cap sets, Dion Gijswijt, Ernie Croot, Jordan Ellenberg, Peter Pach, Seva Lev.
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More Math from Facebook
David Conlon pointed out to two remarkable papers that appeared on the arxive: Joel Moreira solves an old problem in Ramsey’s theory. Monochromatic sums and products in . Abstract: An old question in Ramsey theory asks whether any finite coloring … Continue reading
Posted in Combinatorics, Mathematics over the Internet, Updates
Tagged Ernie Croot, Joel Moreira, Peter Pach, Vsevolod Lev
3 Comments
The Erdős Szekeres polygon problem – Solved asymptotically by Andrew Suk.
Here is the abstract of a recent paper by Andrew Suk. (I heard about it from a Facebook post by Yufei Zhao. I added a link to the original Erdős Szekeres’s paper.) Let ES(n) be the smallest integer such that … Continue reading
