Monthly Archives: July 2008

A Diamater Problem for Families of Sets.

Posted on July 30, 2008 by Gil Kalai

Let me draw your attention to the following problem: Consider a family of subsets of size d of the set N={1,2,…,n}. Associate to a graph as follows: The vertices of  are simply the sets in . Two vertices and are adjacent … Continue reading →

Posted in Combinatorics, Convex polytopes, Open problems | 10 Comments

Extremal Combinatorics II: Some Geometry and Number Theory

Posted on July 17, 2008 by Gil Kalai

Extremal problems in additive number theory Our first lecture dealt with extremal problems for families of sets. In this lecture we will consider extremal problems for sets of real numbers, and for geometric configurations in planar Euclidean geometry. Problem I: Given a set A of … Continue reading →

Posted in Combinatorics, Open problems | Tagged , , | 9 Comments

Michal Linial – An Ambassador in Singapore

Posted on July 16, 2008 by Gil Kalai

After the wonderful “being a cosmonaut” taxi-story, I am happy to present you:  An Ambassador in Singapore A story by Michal Linial It was a long trip, 4 days in Singapore. I visited the tallest artificial waterfall in the world, and … Continue reading →

Posted in Guest blogger, Taxi-and-other-stories | Tagged | 7 Comments

Arrow’s Economics 1

Posted on July 15, 2008 by Gil Kalai

The annual Summer School in Economics at HU was directed until last year by Kenneth Arrow, along with Eyal Winter. Arrow decided this year to step down as a director and Eric Maskin is replacing him. The 2008 Summer School was … Continue reading →

Posted in Economics, Open problems | Tagged , | 12 Comments

Pushing Behrend Around

Posted on July 10, 2008 by Gil Kalai

Erdos and Turan asked in 1936: What is the largest subset of {1,2,…,n} without a 3-term arithmetic progression? In 1946 Behrend found an example with  Now, sixty years later, Michael Elkin pushed the the factor from the denominator to the enumerator, … Continue reading →

Posted in Combinatorics, Updates | Tagged , , | 17 Comments

From Helly to Cayley IV: Probability

Posted on July 6, 2008 by Gil Kalai

I decided to split long part III into two parts. This (truly) last part of this series deals with probabilistic problems and with combinatorial questions regarding higher Laplacians.  21. Higher Laplacians and their meanings Our high dimensional extension to Cayley’s … Continue reading →

Posted in Combinatorics, Probability | 9 Comments

A New Rector-Elect at the Hebrew University of Jerusalem

Posted on July 4, 2008 by Gil Kalai

  Professor Sarah Stroumsa On Wednesday, the Senate of the Hebrew University of Jerusalem elected Professor Sarah Stroumsa (homepage) as the next Rector (provost) of the Hebrew University. For the first time since its establishment, the Hebrew University has elected a woman to its highest post … Continue reading →

Posted in Poetry, Women in science | Tagged , , , , , | 4 Comments

Helly, Cayley, Hypertrees, and Weighted Enumeration III

Posted on July 3, 2008 by Gil Kalai

This is the third and last part of the journey from a Helly type conjecture of Katchalski and Perles to a Cayley’s type formula for “hypertrees”.  (On second thought I decided to divide it into two devoting the second to probabilistic questions.) … Continue reading →

Posted in Combinatorics, Convexity, Open problems, Probability | 8 Comments