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 Alef Corner: ICM2022
 The probabilistic proof that 2^400593 is a prime: a revolutionary new type of mathematical proof, or not a proof at all?
 With Avi at Suzanna
 Meeting Michael H. at Rio
 What is mathematics (or at least, how it feels)
 Alef’s Corner
 To cheer you up in difficult times 22: some mathematical news! (Part 1)
 Cheerful News in Difficult Times: The Abel Prize is Awarded to László Lovász and Avi Wigderson
 Amazing: Feng Pan and Pan Zhang Announced a Way to “Spoof” (Classically Simulate) the Google’s Quantum Supremacy Circuit!
Top Posts & Pages
 Alef Corner: ICM2022
 The probabilistic proof that 2^400593 is a prime: a revolutionary new type of mathematical proof, or not a proof at all?
 TYI 30: Expected number of Dice throws
 Cheerful News in Difficult Times: The Abel Prize is Awarded to László Lovász and Avi Wigderson
 The Argument Against Quantum Computers  A Very Short Introduction
 Answer: Lord Kelvin, The Age of the Earth, and the Age of the Sun
 With Avi at Suzanna
 To cheer you up in difficult times 11: Immortal Songs by Sabine Hossenfelder and by Tom Lehrer
 To cheer you up in difficult times 22: some mathematical news! (Part 1)
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Category Archives: Open problems
Open problem session of HUJICOMBSEM: Problem #5, Gil Kalai – the 3ᵈ problem
This post continues to describe problems presented at our open problems session back in November 2020. Here is the first post in the series. Today’s problem was presented by me, and it was an old 1989 conjecture of mine. A … Continue reading
Open problem session of HUJICOMBSEM: 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
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 3term 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 Péter Pál Pach, Richárd Palincza
9 Comments
Kelman, Kindler, Lifshitz, Minzer, and Safra: Towards the EntropyInfluence Conjecture
Let me briefly report on a remarkable new paper by Esty Kelman, Guy Kindler, Noam Lifshitz, Dor Minzer, and Muli Safra, Revisiting BourgainKalai and Fourier Entropies. The paper describes substantial progress towards the EntropyInfluence conjecture, posed by Ehud Friedgut and … Continue reading
Posted in Combinatorics, Computer Science and Optimization, Open problems
Tagged Dor Minzer, Esty Kelman, Guy Kindler, Muli Safra, Noam Lifshitz
1 Comment
Ringel Conjecture, Solved! Congratulations to Richard Montgomery, Alexey Pokrovskiy, and Benny Sudakov
Ringel’s conjecture solved (for sufficiently large n) A couple weeks ago and a few days after I heard an excellent lecture about it by Alexey Pokrovskiy in Oberwolfach, the paper A proof of Ringel’s Conjecture by Richard Montgomery, Alexey Pokrovskiy, … Continue reading
Posted in Combinatorics, Open problems, Updates
Tagged Alexey Pokrovskiy, Benny Sudakov, Richard Montgomery
3 Comments
Test your intuition 43: Distribution According to Areas in Top Departments.
In the community of mamathetitians in a certain country there are mamathetitians in two areas: Anabra (fraction p of the mamathetitians) and Algasis (fraction 1p of mamathetitians.) There are ten universities with 50 faculty members in each mamathetics department … Continue reading
Posted in Combinatorics, Open problems, Probability, Test your intuition
Tagged Test your intuition
9 Comments
Gérard Cornuéjols’s baker’s eighteen 5000 dollars conjectures
Gérard Cornuéjols Gérard Cornuéjols‘s beautiful (and freely available) book from 2000 Optimization: Packing and Covering is about an important area of combinatorics which is lovely described in the preface to the book The integer programming models known as set packing … Continue reading
Richard Ehrenborg’s problem on spanning trees in bipartite graphs
Richard Ehrenborg with a polyhedron In the Problem session last Thursday in Oberwolfach, Steve Klee presented a beautiful problem of Richard Ehrenborg regarding the number of spanning trees in bipartite graphs. Let be a bipartite graph with vertices on one … Continue reading
A sensation in the morning news – Yaroslav Shitov: Counterexamples to Hedetniemi’s conjecture.
Two days ago Nati Linial sent me an email entitled “A sensation in the morning news”. The link was to a new arXived paper by Yaroslav Shitov: Counterexamples to Hedetniemi’s conjecture. Hedetniemi’s 1966 conjecture asserts that if and are two … Continue reading
Posted in Combinatorics, Open problems, Updates
Tagged Hedetniemi's conjecture, Yaroslav Shitov
17 Comments
Cohen, Haeupler, and Schulman: Explicit Binary TreeCodes & Cancellations
The highdimensional conference in Jerusalem is running with many exciting talks (and they are videotaped), and today in Tel Aviv there is a conference on Optimization and Discrete Geometry : Theory and Practice. Today in Jerusalem, Leonard Schulman talked (video available!) … Continue reading