Author Archives: Gil Kalai

A Breakthrough by Maryna Viazovska Leading to the Long Awaited Solutions for the Densest Packing Problem in Dimensions 8 and 24

Maryna Viazovska The news Maryna Viazovska has solved the densest packing problem in dimension eight! Subsequently, Maryna Viazovska with Henry Cohn, Steve Miller, Abhinav Kumar, and Danilo Radchenko solved the densest packing problem in 24 dimensions! Here are the links to … Continue reading

Posted in Combinatorics, Geometry, Updates | Tagged , , , , , , | 15 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

Polymath 10 Post 3: How are we doing?

The main purpose of this post is to start a new research thread for Polymath 10  dealing with the Erdos-Rado Sunflower problem.  (Here are links to post 2 and post 1.) Here is a  very quick review of where we … Continue reading

Posted in Combinatorics, Mathematics over the Internet, Open problems, Polymath10 | Tagged , | 103 Comments

Polymath10, Post 2: Homological Approach

We launched polymath10 a week ago and it is time for the second post. In this post I will remind the readers what  the Erdos-Rado Conjecture and the Erdos-Rado theorem are,  briefly mention some points made in the previous post and in … Continue reading

Posted in Combinatorics, Polymath10 | Tagged , , , | 125 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

Convex Polytopes: Seperation, Expansion, Chordality, and Approximations of Smooth Bodies

I am happy to report on two beautiful results on convex polytopes. One disproves an old conjecture of mine and one proves an old conjecture of mine. Loiskekoski and Ziegler: Simple polytopes without small separators. Does Lipton-Tarjan’s theorem extends to high … Continue reading

Posted in Combinatorics, Convex polytopes | Tagged , , , , | 1 Comment

Igor Pak’s collection of combinatorics videos

The purpose of this short but valuable post is to bring to your attention Igor Pak’s Collection of Combinatorics Videos

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EDP Reflections and Celebrations

The Problem In 1932, Erdős conjectured: Erdős Discrepancy Conjecture (EDC)  [Problem 9 here] For any constant , there is an such that the following holds. For any function , there exists an   and a   such that For any , … Continue reading

Posted in Combinatorics, Number theory | Tagged , | 4 Comments

Séminaire N. Bourbaki – Designs Exist (after Peter Keevash) – the paper

Update: Nov 4, 2015: Here is the final version of the paper: Design exists (after P. Keevash). On June I gave a lecture on Bourbaki’s seminare devoted to Keevash’s  breakthrough result on the existence of designs. Here is a draft of the … Continue reading

Posted in Combinatorics | Tagged , | 4 Comments