Monthly Archives: November 2020

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.

Posted on November 27, 2020 by Gil Kalai

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 →

Posted in Combinatorics, Geometry | Tagged , , , , , , , | Leave a comment

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

Posted on November 25, 2020 by Gil Kalai

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 | 3 Comments

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

Posted on November 20, 2020 by Gil Kalai

  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 , | 9 Comments

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

Posted on November 17, 2020 by Gil Kalai

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 →

Posted in Combinatorics | Tagged , , , , | 7 Comments

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

Posted on November 14, 2020 by Gil Kalai

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 , , , | 4 Comments

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

Posted on November 10, 2020 by Gil Kalai

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 →

Posted in Combinatorics, Games, Probability, Rationality | Tagged , | 6 Comments