Search Results for: sunflower conjecture

Amazing: Ryan Alweiss, Shachar Lovett, Kewen Wu, Jiapeng Zhang made dramatic progress on the Sunflower Conjecture

WOW! The new paper https://arxiv.org/abs/1908.08483 improved bounds for the sunflower lemma gives the most dramatic progress on the sunflower conjecture since it was asked. Congratulations to Ryan Alweiss, Shachar Lovett, Kewen Wu, Jiapeng Zhang. (Written on my smartphone will expand … Continue reading

Posted in Combinatorics, Uncategorized | 8 Comments

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

Posted in Combinatorics, Mathematics over the Internet, Open problems, Polymath10 | Tagged , | 6 Comments

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

Posted in Combinatorics, Polymath10 | Tagged , , , | 36 Comments

Mohammad Ghomi and Joel Spruck settled the Cartan-Hadamard conjecture!

Greetings from Oberwolfach from a great conference on algebraic, geometric, and topological combinatorics. Stay tuned for more pictures and updates from Oberwolfach and CERN, and also in case you did not see it already here is the link to the … Continue reading

Posted in Geometry, Uncategorized | Tagged , , | 5 Comments

Polymath10: The Erdos Rado Delta System Conjecture

The purpose of this post is to start the polymath10 project. It is one of the nine projects (project 3d) proposed by Tim Gowers in his post “possible future polymath projects”. The plan is to attack Erdos-Rado delta system conjecture also known as the … Continue reading

Posted in Combinatorics, Polymath10 | Tagged , , , | 141 Comments

Cap Sets, Sunflowers, and Matrix Multiplication

This post follows a recent paper On sunflowers  and matrix multiplication by Noga Alon, Amir Spilka, and Christopher Umens (ASU11) which rely on an earlier paper Group-theoretic algorithms for matrix multiplication, by Henry Cohn, Robert Kleinberg, Balasz Szegedy, and Christopher Umans (CKSU05), … Continue reading

Posted in Combinatorics, Computer Science and Optimization, Open problems | Tagged , , , , , , | 9 Comments

Amazing! Keith Frankston, Jeff Kahn, Bhargav Narayanan, Jinyoung Park: Thresholds versus fractional expectation-thresholds

This post describes a totally unexpected breakthrough about expectation and thresholds. The result  by Frankston, Kahn, Narayanan, and Park has many startling applications and it builds on the recent breakthrough work of Alweiss, Lovett, Wu and Zhang on the sunflower … Continue reading

Posted in Combinatorics, Probability | Tagged , , , | 3 Comments

Noisy quantum circuits: how do we know that we have robust experimental outcomes at all? (And do we care?)

In a recent post we discussed Google’s claim of achieving “quantum supremacy” and my reasons to think that these claims will not stand. (See also this comment for necessary requirements from a quantum supremacy experiment.) This debate gives a good … Continue reading

Posted in Computer Science and Optimization, Quantum | Tagged , , | 10 Comments

Computer Science and its Impact on our Future

A couple of weeks ago I told you about Avi Wigderson’s vision on the connections between the theory of computing and other areas of mathematics on the one hand and between computer science and other areas of science, technology and … Continue reading

Posted in Academics, Computer Science and Optimization, Quantum, Updates | Tagged | 1 Comment

Polymath10 conclusion

The Polymath10 project on the Erdos-Rado Delta-System conjecture took place over this blog from November 2015 to May 2016. I aimed for an easy-going project that people could participate calmly aside from their main research efforts and  the duration of … Continue reading

Posted in Combinatorics, Open problems, Polymath10 | Tagged , | 5 Comments