Clik here to view.
Richard Montgomery presents: A proof of the Ryser-Brualdi-Stein conjecture...
Fresh from the ArXiv A proof of the Ryser-Brualdi-Stein conjecture for large even n by Richard Montgomery A Latin square of order n is an n by n grid filled using n symbols so that each symbol appears...
View ArticleClik here to view.
ChatGPT Meets Elchanan Mossel’s Dice Problem
One of the greatest hits of this blog was Elchanan Mossel’s dice problem, asked here and answered here. Here is how chatGPT (the free version) handles the problem. You throw a die until you get 6. What...
View ArticleClik here to view.
Marton’s “Polynomial Freiman-Ruzsa” Conjecture was Settled by Tim Gowers, Ben...
Gowers, Green, Manners and Tao. They reminded me of the A-team of the 1980s television series: “If you have a problem, if no one else can help, and if you can find them, maybe you can hire… the...
View ArticleClik here to view.
Progress Around Borsuk’s Problem
I was excited to see the following 5-page paper: Convex bodies of constant width with exponential illumination number by Andrii Arman, Andrii Bondarenko, and Andriy Prymak Abstract: We show that there...
View ArticleClik here to view.
Oberwolfach Workshop: Geometric Algebraic and Topological Combinatorics 2023,...
This week I participate (remotely) in an exciting Oberwolfach meeting on Geometric Algebraic and Topological Combinatorics. See this post about a whole sequence of related meetings. Let me tell you...
View ArticleClik here to view.
On Viazovska’s modular form inequalities by Dan Romik
The main purpose of this post is to tell you about a recent paper by Dan Romik which gives a direct proof of two crucial inequalities in Maryna Viazovska’s proof that lattice sphere packing is the...
View ArticleClik here to view.
Marcelo Campos, Matthew Jenssen, Marcus Michelen and, and Julian...
A few days ago, a new striking paper appeared on the arXiv A new lower bound for sphere packing by Marcelo Campos, Matthew Jenssen, Marcus Michelen, and Julian Sahasrabudhe Here is the abstract: We...
View ArticleClik here to view.
Fun with Algorithms (FUN 2024)
Fun with Algorithms FUN is a series of conferences dedicated to the use, design, and analysis of algorithms and data structures, focusing on results that are “fun” but also original and...
View ArticleClik here to view.
Soma Villanyi: Every d(d+1)-connected graph is globally rigid in d dimensions.
Today, I want to tell you a little about the following paper that solves a conjecture of Laszlo Lovász and Yechiam Yemini from 1982 and an even stronger conjecture of Bob Connelly, Tibor Jordán, and...
View ArticleClik here to view.
Riddles (Stumpers), Psychology, and AI.
Two months ago I presented five riddles and here, in this post, you will find a few more. (These types of riddles are called by Maya Bar-Hillel “stumpers”.) This time, we will have a discussion about...
View ArticleClik here to view.
TYI 54: A Variant of Elchanan Mossel’s Amazing Dice Paradox
The following question was inspired by recent comments to the post on Elchanan Mossel’s amazing Dice Paradox. A fair dice is a dice that when thrown you get each of the six possibilities with...
View ArticleClik here to view.
On the Limit of the Linear Programming Bound for Codes and Packing
Alex Samorodnitsky The most powerful general method for proving upper bounds for the size of error correcting codes and of spherical codes (and sphere packing) is the linear programming method that...
View ArticleClik here to view.
Yair Shenfeld and Ramon van Handel Settled (for polytopes) the Equality Cases...
The power of negative thinking: Combinatorial and geometric inequalities Two weeks ago, I participated (remotely) in the discrete geometry Oberwolfach meeting, and Ramon van Handel gave a beautiful...
View ArticleClik here to view.
Three Remarkable Quantum Events at the Simons Institute for the Theory of...
In the picture (compare it to this picture in this post) you can see David DiVincenzo’s famous 7-steps road map (from 2000) to quantum computers, with one additional step “quantum supremacy on NISQ...
View ArticleClik here to view.
Updates and Plans IV
A carpet of flowers in Shokeda, near Gaza, a few years ago. This is the fourth post of this type (I (2008); II(2011); III(2015).) I started planning this post in 2019 but as it turned out, earlier...
View ArticleClik here to view.
Plans and Updates: Complementary Pictures
Jerusalem October 4, 2023 The picture on the right is from ~ 60 years ago. Tel Aviv, five sunsets and a horse Efi Arazi school of Computer Science Corona times Tel Aviv (in the balcony – our...
View ArticleClik here to view.
Random Circuit Sampling: Fourier Expansion and Statistics
Our new paper Yosi Rinott, Tomer Shoham and I wrote a new paper on our statistical study of the data from the 2019 Google quantum supremacy experiment. Random Circuit Sampling: Fourier Expansion and...
View ArticleClik here to view.
Updates from Cambridge
I am writing from Cambridge, UK, where I participated in an impressive conference celebrating Tim Gowers’s 60 birthday and I an about to take part in a satellite workshop of Theoretical computer...
View ArticleClik here to view.
Arturo Merino, Torsten Mütze, and Namrata Apply Gliders for Hamiltonicty!
Happy Passover to all our readers On the way from Cambridge to Tel Aviv I had a splendid three hour visit to London (from Kings Cross to UCL and back), where I met my graduate student Gabriel Gendler...
View ArticleClik here to view.
My Notices AMS Paper on Quantum Computers – Eight Years Later, a Lecture by...
The first part of the post is devoted to eight-year anniversary of my 2016 paper. I will go on to describe a recent lecture by Dorit Aharonov and conclude with my toast to Michael Ben-Or. The Quantum...
View Article