Category Archives: Combinatorics

Arturo Merino, Torsten Mütze, and Namrata Apply Gliders for Hamiltonicty!

Posted on April 23, 2024 by Gil Kalai

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 and Freddie … Continue reading →

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

Updates from Cambridge

Posted on April 15, 2024 by Gil Kalai

I am writing from Cambridge, UK, where I participated in an impressive conference celebrating Tim Gowers’s 60 birthday and I am about to take part in a satellite workshop of Theoretical computer science. Coming here was the first time I … Continue reading →

Posted in Combinatorics, Computer Science and Optimization, Conferences | Tagged , | 7 Comments

Updates and Plans IV

Posted on March 20, 2024 by Gil Kalai

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 drafts have quickly … Continue reading →

Posted in Combinatorics, Computer Science and Optimization, Geometry, People, personal, Updates | Tagged , | 1 Comment

Yair Shenfeld and Ramon van Handel Settled (for polytopes) the Equality Cases For The Alexandrov-Fenchel Inequalities

Posted on February 7, 2024 by Gil Kalai

Two weeks ago, I participated (remotely) in the discrete geometry Oberwolfach meeting, and Ramon van Handel gave a beautiful lecture about the equality cases of Alexandrov-Fenchel inequalities which is among the most famous problems in convex geometry. In the top … Continue reading →

Posted in Combinatorics, Convexity, Geometry | Tagged , , , , | 2 Comments

On the Limit of the Linear Programming Bound for Codes and Packing

Posted on January 21, 2024 by Gil Kalai

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 goes back to Philippe Delsarte. There are very interesting … Continue reading →

Posted in Combinatorics, Convexity, Geometry | Tagged , , , | 2 Comments

Soma Villanyi: Every d(d+1)-connected graph is globally rigid in d dimensions.

Posted on January 1, 2024 by Gil Kalai

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 Walter Whiteley from 2013: Every … Continue reading →

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

Marcelo Campos, Matthew Jenssen, Marcus Michelen and, and Julian Sahasrabudhe: Striking new Lower Bounds for Sphere Packing in High Dimensions

Posted on December 20, 2023 by Gil Kalai

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 show there exists a packing of … Continue reading →

Posted in Combinatorics, Convexity, Geometry | Tagged , , , , , | 5 Comments

On Viazovska’s modular form inequalities by Dan Romik

Posted on December 17, 2023 by Gil Kalai

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 densest sphere packing in … Continue reading →

Posted in Combinatorics, Convexity, Geometry, Number theory | Tagged , , , | 4 Comments

Oberwolfach Workshop: Geometric Algebraic and Topological Combinatorics 2023, part I

Posted on December 14, 2023 by Gil Kalai

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 first about the first two lectures. Federico Ardila,  Recent developments … Continue reading →

Posted in Combinatorics, Conferences | 2 Comments

Marton’s “Polynomial Freiman-Ruzsa” Conjecture was Settled by Tim Gowers, Ben Green, Freddie Manners and Terry Tao

Posted on November 13, 2023 by Gil Kalai

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 A-Team.” A … Continue reading →

Posted in Combinatorics, Number theory, Updates | Tagged , , , , | 10 Comments