Category Archives: Combinatorics

The Argument Against Quantum Computers – A Very Short Introduction

Left: Gowers’s book Mathematics a very short introduction. Right C. elegans; Boson Sampling can be seen as the C. elegans of quantum computing. (See, this paper.) Update (January 6, 2021): Tomorrow January, 7, 8:30 AM Israel time, I give a … Continue reading

Posted in Combinatorics, Computer Science and Optimization, Physics, Probability, Quantum | Tagged , | 7 Comments

Open problem session of HUJI-COMBSEM: Problem #4, Eitan Bachmat: Weighted Statistics for Permutations

This is a continuation of our series of posts on the HUJI seminar 2020 open problems. This time the post was kindly written by Eitan Bachmat who proposed the problem.  My summary: understanding of the distribution of largest increasing subsequences … Continue reading

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To Cheer You Up in Difficult Times 15: Yuansi Chen Achieved a Major Breakthrough on Bourgain’s Slicing Problem and the Kannan, Lovász and Simonovits Conjecture

This post gives some background to  a recent amazing breakthrough  paper: An Almost Constant Lower Bound of the Isoperimetric Coefficient in the KLS Conjecture by Yuansi Chen. Congratulations Yuansi! The news Yuansi Chen gave an almost constant bounds for Bourgain’s … Continue reading

Posted in Combinatorics, Computer Science and Optimization, Convexity, Geometry | Tagged | 5 Comments

Open problem session of HUJI-COMBSEM: Problem #3, Ehud Friedgut – Independent sets and Lionel Levine’s infamous hat problem.

Here are the two problems presented by Ehud Friedgut. The first arose by Friedgut, Kindler, and me in the context of studying  Lionel Levine’s infamous hat problem. The second is Lionel Levine’s infamous hat problem. Ehud Friedgut with a few … Continue reading

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Open problem session of HUJI-COMBSEM: Problem #2 Chaya Keller: The Krasnoselskii number

  Marilyn Breen This is our second post on the open problem session of the HUJI combinatorics seminar. The video of the session is here. Today’s problem was presented by Chaya Keller. The Krasnoselskii number One of the best-known applications … Continue reading

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Photonic Huge Quantum Advantage ???

This is a quick and preliminary post about a very recent announcement in a Science Magazine paper: Quantum computational advantage using photons by a group of researchers leaded by Jianwei Pan and Chao-Yang Lu. (Most of the researchers are from … Continue reading

Posted in Combinatorics, Physics, Probability, Quantum | Tagged , | 12 Comments

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 | 2 Comments

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 , | 9 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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