Monthly Archives: June 2011

Around Borsuk’s Conjecture 1: Some Problems

Posted on June 30, 2011 by Gil Kalai

Greetings to all! Karol Borsuk conjectured in 1933 that every bounded set in can be covered by sets of smaller diameter. In a previous post I described the counterexample found by Jeff Kahn and me. I will devote a few posts … Continue reading →

Posted in Combinatorics, Convexity | Tagged , | 11 Comments

The Combinatorics of Cocycles and Borsuk’s Problem.

Posted on June 15, 2011 by Gil Kalai

Cocycles Definition:  A -cocycle is a collection of -subsets such that every -set contains an even number of sets in the collection. Alternative definition: Start with a collection of -sets and consider all -sets that contain an odd number of members … Continue reading →

Posted in Combinatorics, Convexity, Open problems | Tagged , , , , | 3 Comments

Tentative Plans and Belated Updates II

Posted on June 14, 2011 by Gil Kalai

Elementary school reunion: Usually, I don’t write about personal matters over the blog, but having (a few weeks ago) an elementary school reunion after 42 years was a moving and exciting event as to consider making an exception. For now, here … Continue reading →

Posted in Updates | Tagged , , , | 8 Comments

Another way to Revolutionize Football

Posted on June 9, 2011 by Gil Kalai

The angle of Victoria Beckham’s hat (here in a picture from a recent wedding) is closely related to our previous post on football One of the highlights of the recent Newton Institute  conference on discrete harmonic analysis was a football … Continue reading →

Posted in Games, Mathematics to the rescue, Sport | Tagged , | 9 Comments