## סדנא לתלמידי בוגר מצטיינים במתמטיקה

### מכון איינשטיין למתמטיקה, האוניברסיטה העברית בירושלים

יום א’ י”ז אלול – יום ה’ כ”ח אלול תשס”ט

6-17/9/09

המכון למתמטיקה של האוניברסיטה העברית מזמין תלמידי מתמטיקה מצטיינים המסיימים שנה ב’ או ג’ של לימודיהם במוסדות להשכלה גבוהה, ומעוניינים להמשיך במחקר מתמטי, לסדנה בת שבועיים שתתקיים בקמפוס ספרא של האוניברסיטה העברית בגבעת רם, ירושלים, בשבועיים שלפני ראש השנה תש”ע.

# The Generation Gap

Which is larger, the generation gap between you and your perents or the generation gap between you and your children?

# A Proposal Regarding Gilad Shalit

Since an agreement for the release of Gilad Shalit in exchange for the release of Hamas prisoners could not be reached, I propose to initiate negotiations (perhaps with Egyptian help) on the improvement of Gilad Shalit’s captivity conditions.

In return for letting Shalit have frequent visits of the red cross,  letter exchange and perhaps also visits by his family, Israel can offer the release  of many dozens of prisoners, such as Hamas Parliament members, and other prisoners not directly involved in violent activities.

# Colloquium at Berlin

I arrived to Berlin for a short visit to give a colloquium talk at the new BMS on Helly-type theorems, and to participate in the Ph. D. committee of  Ronald Wotzlaw. (Update: Dr. Ronald Wotzlaw.)

Here is an abstract for the talk decorated (it may take me a few days) with links to some earlier posts where matters are described in details, and also with some external links.

Helly’s theorem from 1912 asserts that for a finite family of convex sets in a d-dimensional Euclidean space, if every d+1 of the sets have a point in common then all of the sets have a point in common.
This theorem found applications in many areas of mathematics and led to numerous generalizations. Helly’s theorem is closely related to two other fundamental theorems in convexity: Radon’s theorem asserts that a set of d+2 points in d-dimensional real space can be divided into two disjoint sets whose convex hulls have non empty intersection. Caratheodory’s theorem asserts that if S is a set in d-dimensional real space and x belongs to its convex hull then x already belongs to the convex hull of at most d+1 points in S.

The first part of the lecture will discuss the basic relation between Helly, Radon, and Caratheodory’s theorems. Those are described in this post We move to discuss several quantitative generalizations of the theorem. At first we will consider what happens to the theorem if we replace the condition “non-empty intersection” by “the dimension of the intersection is at least r. (Question: What is the answer for r=1?)

Meir Katchalski settled this problem for every d and r Continue reading

A transparency and a lecture using transparencies. (No relation to the advice.)

### Worst – The same as above except that the transparencies are handwritten in an unreadable way.

Q: What do Yehuda Agnon, Michael Ben-Or, Ehud Lehrer, Uzi Segal (whose calibration theorem was mentioned in the post on the controversy around expected utility theory), Mike Werman, myself, and quite a few others, all have in common?

Hint:

Answer: We all, (and altogether more than 20 students) took part in Continue reading

# New Haven (mainly pictures)

Yale, New Haven

I am back in New Haven which have become my home away from home in the last five years.

Cappuccino’S and more – Cedar cross Congress, New Haven. Not only that this name is similar to my blog’s name, but throwing in as many s’s and apostrphees reflects also my approach to the English grammer.

# 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 $n^{\log d}$ but my proof only gave $d^{\log n},$

It was a pleasant surprise to note that $n^{\log d}=d^{\log n}$.

### 2. A bigger surprise

A few weeks ago James Lee gave a talk and proved a bound of the form $(\log n)^{\log \log \log n}.$  I was surprised to learn from him that $(\log n)^{\log \log \log n} = ( \log \log n)^{\log \log n} .$

(Update: I got it wrong at first, thanks guys)

This is an even more surprising special case of the formula above.

### 3.  Is it better to have the discount first?

Question: What is a better deal: A store that gives 12% student-discount after it adds a 12% value added tax to the price of the product? Or a store that first adds 12% tax on the entire sum and only then deducts 12% student discount?

Ohh, The way I asked this question the two alternatives are precisely the same. Let me ask it again: What is a better deal: A store that gives 12% student discount after adding a 12% value added tax to the price of the product? Or a store that first deducts the 12% student discount, and only then adds 12% tax on the new price?