Monthly Archives: August 2008

A Diameter Problem (2)

2. The connection with Hirsch’s Conjecture The Hirsch Conjecture asserts that the diameter of the graph G(P) of a d-polytope P with n facets is at most n-d. Not even a polynomial upper bound for the diameter in terms of d and … Continue reading

Posted in Combinatorics, Convex polytopes, Open problems | 5 Comments

Two Very Early Problems, a Simple Solution, and a New Problem

    As an undergraduate student whenever I studied some subject I tried to come up with problems. Many of these problems were artificial or silly and, of course, I forgot most of them. But a few still make sense. Here are … Continue reading

Posted in Open problems | 9 Comments

Surprising Math

1. A pleasant surprise When I worked on the diameter problem for d-polytopes with n facets. I was aiming to prove an upper  bound of the form but my proof only gave It was a pleasant surprise to note that . 2. … Continue reading

Posted in Uncategorized | 4 Comments

Plans and Updates

Jerusalem and Budapest       Monday, last week was the last day of lectures for the spring term here at the Hebrew U.  One outcome of the long professors’ strike was a very fruitful year for research seminars. We ran them during … Continue reading

Posted in Conferences, Updates | Tagged , , | 4 Comments

More Art: Tami’s Autoportrait

  And in my office, there is a beautiful autoportrait by my sister Tamar Kalai. (Click for a deatiled picture.)  

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Our Department’s Quilt

Academic administation is a topic of great interest that desrves a special post. The highest post I served was as the department chair, and one thing I did was to acquire for the department a quilt by the artist Anna Maria … Continue reading

Posted in Art | Tagged , , , | 1 Comment