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- My Notices AMS Paper on Quantum Computers – Eight Years Later, a Lecture by Dorit Aharonov, and a Toast to Michael Ben-Or
- Arturo Merino, Torsten Mütze, and Namrata Apply Gliders for Hamiltonicty!
- Updates from Cambridge
- Random Circuit Sampling: Fourier Expansion and Statistics
- Plans and Updates: Complementary Pictures
- Updates and Plans IV
- Three Remarkable Quantum Events at the Simons Institute for the Theory of Computing in Berkeley
- Yair Shenfeld and Ramon van Handel Settled (for polytopes) the Equality Cases For The Alexandrov-Fenchel Inequalities
- On the Limit of the Linear Programming Bound for Codes and Packing
Top Posts & Pages
- My Notices AMS Paper on Quantum Computers - Eight Years Later, a Lecture by Dorit Aharonov, and a Toast to Michael Ben-Or
- Amazing: Justin Gilmer gave a constant lower bound for the union-closed sets conjecture
- Arturo Merino, Torsten Mütze, and Namrata Apply Gliders for Hamiltonicty!
- To cheer you up in difficult times 23: the original hand-written slides of Terry Tao's 2015 Einstein Lecture in Jerusalem
- An Aperiodic Monotile
- Marton's "Polynomial Freiman-Ruzsa" Conjecture was Settled by Tim Gowers, Ben Green, Freddie Manners and Terry Tao
- Lovasz's Two Families Theorem
- Extremal Combinatorics VI: The Frankl-Wilson Theorem
- Remarkable New Stochastic Methods in ABF: Ronen Eldan and Renan Gross Found a New Proof for KKL and Settled a Conjecture by Talagrand
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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.
27 Comments
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
8 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