Author Archives: Gil Kalai

Recent progress on high dimensional Turan-Type problems by Andrey Kupavskii, Alexandr Polyanskii, István Tomon, and Dmitriy Zakharov and by Jason Long, Bhargav Narayanan, and Corrine Yap.

The extremal number for surfaces Andrey Kupavskii, Alexandr Polyanskii, István Tomon, Dmitriy Zakharov: The extremal number of surfaces Abstract: In 1973, Brown, Erdős and Sós proved that if is a 3-uniform hypergraph on vertices which contains no triangulation of the sphere, then   … Continue reading

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Open problem session of HUJI-COMBSEM: Problem #1, Nati Linial – Turan type theorems for simplicial complexes.

On November, 2020  we had a very nice open problem session in our weekly combinatorics seminar at HUJI.  So I thought to have a series of posts to describe you the problems presented there.  This is the first post in … Continue reading

Posted in Combinatorics, Geometry, Open problems | Tagged | 1 Comment

Péter Pál Pach and Richárd Palincza: a Glimpse Beyond the Horizon

  Prologue Consider the following problems: P3: What is the maximum density of a set A in without a 3-term AP? (AP=arithmetic progression.) This is the celebrated Cap Set problem and we reported here in 2016 the breakthrough results by … Continue reading

Posted in Combinatorics, Geometry, Number theory, Open problems | Tagged , | 6 Comments

To cheer you up 14: Hong Liu and Richard Montgomery solved the Erdős and Hajnal’s odd cycle problem

The news: In 1981, Paul Erdős and András Hajnal asked whether the sum of the reciprocals of the odd cycle lengths in a graph with infinite chromatic number is necessarily infinite. Hong Liu and Richard Montgomery have just proved that … Continue reading

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To cheer you up in difficult times 13: Triangulating real projective spaces with subexponentially many vertices

Wolfgang Kühnel Today I want to talk about a new result in a newly arXived paper: A subexponential size by Karim Adiprasito, Sergey Avvakumov, and Roman Karasev. Sergey Avvakumov gave about it a great zoom seminar talk about the result … Continue reading

Posted in Algebra, Combinatorics, Geometry | Tagged , , , | 1 Comment

Benjamini and Mossel’s 2000 Account: Sensitivity of Voting Schemes to Mistakes and Manipulations

Here is a popular account by Itai Benjamini and Elchanan Mossel from 2000 written shortly after the 2000 US presidential election. Elchanan and Itai kindly agreed that I will publish it here,  for the first time, 20 years later!  I … Continue reading

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Test Your Intuition (46): What is the Reason for Maine’s Huge Influence?

Very quick updates: Corona: Israel is struggling with the pandemic with some successes,  some failures, and much debate. Peace: We have peace agreements now with several Arab countries, most recently with Sudan. This is quite stunning. Internal politics: As divided … Continue reading

Posted in Games, Probability, Statistics, Test your intuition | Tagged , | 6 Comments

This question from Tim Gowers will certainly cheeer you up! and test your intuition as well!

I've rolled a die and not looked at it yet. The statement, "If the number I rolled equals 2+2 then it equals 5," is … — Timothy Gowers (@wtgowers) October 18, 2020 Here is a tweet from Tim Gowers  It … Continue reading

Posted in Logic and set theory, Philosophy, Probability | Tagged | 12 Comments

Three games to cheer you up.

Here are three cool games prepared by students of my 2020 Game Theory class. Enjoy! (More games will come later. See this post for an earlier game.) Four-in -a-row with HEX board by: Daniella Drori, Margot Guetta, Eyal Magen and … Continue reading

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Cheerful Test Your Intuition (#45): Survey About Sisters and Brothers

You survey many many school children and ask each one: Do you have more brothers than sisters? or more sisters than brothers? or the same number? Then you separate the boys’s answers from the girls’s answers Which of the following … Continue reading

Posted in Combinatorics, Probability, Riddles, Statistics, Test your intuition | Tagged | 7 Comments