Monthly Archives: June 2008

Cosmonaut: Michal Linial

Posted on June 30, 2008 by Gil Kalai

   Ladies and gentelmen, I am very happy to present to you: Being a Cosmonaut A story by Michal Linial I am back from the airport… not in the best mood for a long discussion but quite open to hear … Continue reading →

Posted in Guest blogger, Taxi-and-other-stories | Tagged , | 6 Comments

The Golden Room and the Golden Mountain

Posted on June 27, 2008 by Gil Kalai

  Christine Björner’s words at the Stockholm Festive Combinatorics are now available to all our readers. What makes this moving and interesting, beyond the intimate context of the conference, is our (mathematician’s) struggle (and usually repeated failures) to explain to … Continue reading →

Posted in What is Mathematics | Tagged , | 1 Comment

Amir Ban on Deep Junior

Posted on June 25, 2008 by Gil Kalai

Ladies and Gentelmen: Amir Ban (right, in the picture above) the guest blogger, was an Israeli Olympiad math champion in the early 70s, with Shay Bushinsky he wrote Deep Junior, and he is also one of the inventors of the “disc on … Continue reading →

Posted in Games, Guest blogger | Tagged , , , | 15 Comments

Tel-Aviv’s “Jerusalem Beach”

Posted on June 24, 2008 by Gil Kalai

  Friday’s evening at the beach Late Friday afternoon, and the “Jerusalem beach” in Tel Aviv is still quite crowded with young and old people, families and singles, tourists, foreign workers and Israelis. The sea is calm and beautiful and the Tel … Continue reading →

Posted in Taxi-and-other-stories, Updates | Tagged , | 5 Comments

Euler’s Formula, Fibonacci, the Bayer-Billera Theorem, and Fine’s CD-index

Posted on June 22, 2008 by Gil Kalai

Bill Gessley proving Euler’s formula (at UMKC) In the earlier post about Billerafest I mentioned the theorem of Bayer and Billera on flag numbers of polytopes. Let me say a little more about it. 1. Euler Euler’s theorem asserts that for … Continue reading →

Posted in Combinatorics, Convex polytopes | Tagged , , , , , | 8 Comments

Helly’s Theorem, “Hypertrees”, and Strange Enumeration II: The Formula

Posted on June 18, 2008 by Gil Kalai

In the first part of this post we discussed an appealing conjecture regaring an extension of Cayley’s counting trees formula. The number of d-dimensional “hypertrees” should somehow add up  to . But it was not clear to us which complexes we want … Continue reading →

Posted in Combinatorics, Convexity | Tagged , , | 7 Comments

Optimism – two quotes

Posted on June 15, 2008 by Gil Kalai

1. Here is a quote from Karl Popper’s paper “Science, Problems, Aims, Responsibilities” about Francis Bacon: “According to Bacon, nature, like God, was present in all things, from the greatest to the least. And it was the aim or the … Continue reading →

Posted in Philosophy | Tagged , , , | 3 Comments

Billerafest

Posted on June 12, 2008 by Gil Kalai

I am unable to attend the conference taking place now at Cornell, but I send my warmest greetings to Lou from Jerusalem. The titles and abstracts of the lectures can be found here. Let me tell you about two theorems by Lou. … Continue reading →

Posted in Conferences, Convex polytopes | Tagged , , , | 1 Comment

Helly’s Theorem, “Hypertrees”, and Strange Enumeration I

Posted on June 10, 2008 by Gil Kalai

1. Helly’s theorem and Cayley’s formula Helly’s theorem asserts: For a family of n convex sets in , n > d, if every d+1 sets in the family have a point in common then all members in the family have a point in common. … Continue reading →

Posted in Combinatorics, Convexity | Tagged , , , , | 11 Comments

A Small Debt Regarding Turan’s Problem

Posted on June 9, 2008 by Gil Kalai

Turan’s problem asks for the minimum number of triangles on n vertices so that every 4 vertices span a triangle. (Or equivalently, for the maximum number of triangles on n vertices without a “tetrahedron”, namely without having four triangles on … Continue reading →

Posted in Combinatorics | Tagged , | 3 Comments