Search Results for: erdos

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 , | Leave a comment

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 , , , | 26 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 , , , | 137 Comments

Erdős Lectures 2014 – Dan Spielman

Image | Posted on by | Tagged , | 1 Comment

Erdős’ Birthday

Paul Erdős was born on March 26, 1913 2013 a hundred years ago. This picture (from Ehud Friedgut’s homepage) was taken in September ’96 in a Chinese restaurant in Warsaw, a few days before Paul Erdős passed away. The other diners are Svante Janson, Tomasz Łuczack and … Continue reading

Posted in Combinatorics | Tagged | 3 Comments

János Pach: Guth and Katz’s Solution of Erdős’s Distinct Distances Problem

Click here for the most recent polymath3 research thread. Erdős and Pach celebrating another November day many years ago. The Wolf disguised as Little Red Riding Hood. Pach disguised as another Pach. This post is authored by János Pach A … Continue reading

Posted in Combinatorics, Geometry, Guest blogger, Open problems | Tagged , | 13 Comments

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 , , , , , | 18 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 , , , | 3 Comments

Polymath10-post 4: Back to the drawing board?

It is time for a new polymath10 post on the Erdos-Rado Sunflower Conjecture. (Here are the links for post1, post2, post3.) Let me summarize the discussion from Post 3 and we can discuss together what directions to peruse. It is … Continue reading

Posted in Combinatorics, Mathematics over the Internet, Polymath10 | 11 Comments

News (mainly polymath related)

Update (Jan 21) j) Polymath11 (?) Tim Gowers’s proposed a polymath project on Frankl’s conjecture. If it will get off the ground we will have (with polymath10) two projects running in parallel which is very nice. (In the comments Jon Awbrey gave … Continue reading

Posted in Combinatorics, Conferences, Mathematics over the Internet, Polymath10, Polymath3, Updates | Tagged , , , , , , , | 11 Comments