Author Archives: Gil Kalai

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 , , , | 62 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 , , , | 121 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

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Important formulas in Combinatorics

Another spin-off of the Noga-poster-formula-competition is a MathOverflow question:  Important formulas in combinatorics. The question collects important formulas representing major progress in combinatorics. So far there are 31 formulas and quite a few were new to me. There are several areas … Continue reading

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Updates and plans III.

Update on the great Noga’s Formulas competition. (Link to the original post, many cash prizes are still for grab!) This is the third “Updates and plans post”. The  first one was from 2008 and the  second one from 2011. Updates: Combinatorics and … Continue reading

Posted in Combinatorics, Conferences, Updates | 6 Comments

NogaFest, NogaFormulas, and Amazing Cash Prizes

Ladies and gentlemen,  a conference celebrating Noga Alon’s 60th birthday is coming on January. It will take place at Tel Aviv University on January 17-21. Here is the event webpage. Don’t miss the event !  Cash Prizes! The poster includes 15 … Continue reading

Posted in Combinatorics, Conferences, Updates | Tagged , | 27 Comments

Carmella Kalai (1926-2015)

My beloved mother Carmella Kalai passed away last week. With me, 1956 My father Hanoch Kalai, my mother Carmella, My sister Tamar (Tami) and me around 1957).

Posted in Art, Obituary, personal, Updates | Tagged | 2 Comments