November 6, 2003: 
Boris Levant,  Halasz's Lemma on the concentration of signed sums of vectors 
(after Oskolkov)


November 13, 2003: 
Boris Levant,  continuation


November 20, 2003: 
Limor Ben-Efraim,  Optimal Numberings and Isoperimetric Problems on Graphs 
(after  L.H. Harper)
In the talk I will present the article of  Harper which solve the following problem: 
How may be the numbers 1, 2, ..., 2^{n} be assigned to the 2^{n} vertices of the 
n-cube so that the maximum absolute difference of numbers assigned to the opposite 
ends of the same edge is minimized? 
Through the proof of the above problem he solved also the Isoperimetric problem 
of finding the sets with minimal boundary on the n-cube.


November 27, 2003: 
Limor  will finish her lecture. Then:
Dvir Kleper,  The fix point property for spaces with unconditional bases 
(after Lin and others).  


December 4, 2003: 
Dvir Kleper, continuation.


December 11, 2003: 
Emanuel Milman, Symmetrization and Isotropic Constants of Convex Bodies
(after J. Bourgain, B. Klartag and V. Milman).
We will review the above titled article, which reduces the problem of 
bounding the isotropic constant of general convex bodies, to the problem 
of bounding it on bodies having bounded volume ratio.

December 25, 2003
Shiri Artstein, Ehrhard inequality for general sets (a Gaussian version of the
Brunn-Minkowski inequality) and the Brascamp-Lieb inequality via solutions
of the heat equation (after the works of Borell and Barthe-Cordero).

January 1, 2004
Limor Ben-Efraim, Frankl and Furedi's proof of Harper's isoperimetric theorem for the discrete
cube.

March 4, 2004
an Romik, The geometry of the Sierpinski gasket
Abstract: This will be an informal talk, in which I will survey some
fundamental definitions and results on self-similar fractals,
concentrating on the Sierpinski gasket as a well-studied example. I will
describe the open problem of determining the precise value of the
Hausdorff measure of the Sierpinski gasket, related to an isodiametric
problem, and show some upper bounds due to Zhou and Feng. I will also
construct a natural subset of the cartesian product of the gasket with
itself that has Hausdorff dimension log((5+sqrt(17))/2)/log(2).

March 11, 2004
Boaz Klartag, An isomorphic version of the slicing problem
Abstract: We will show that any centrally symmetric
convex body $K \subset \RR^n$ has a perturbation $T \subset \RR^n$
which is convex and centrally symmetric, such that the isotropic
constant of $T$ is universally bounded. $T$ is close to $K$ in the
sense that the Banach-Mazur distance between $T$ and $K$ is
$O(\log n)$. If $K$ has a non-trivial type then the distance is
universally bounded. In addition, if $K \subset \RR^n$ is
quasi-convex then there exists a quasi-convex $T \subset \RR^n$
with a universally bounded isotropic constant and with a
universally bounded distance to $K$. Our technique involves use of
mixed volumes and Aleksandrov-Fenchel inequalities. If time permits,
some additional consequences of this technique will be presented.


March 18, 2004
Gidi Amir, The cautious walk.
  We study the "cautious" walk - an excited random
  walk on $\Z^3_+$, which gets a push downward each time
  it reaches a new vertex, and behaves like a Simple random walk
  when  it reaches a vertex it has visited before.
  (With reflection upward on the plane $z=0$).
  We analyze the case where the push received is
  deterministic - i.e. each time a new vertex is
  reached, the walker goes down with probability 1,
  and show that this walk is recurrent. We also analyze
  it's behaviour in terms of number of returns to 0.
  (Joint with Itai Binjamini and Gady Kozma)


March 25, 2004:
Dvir Kleper, On a fixed point theorem of Maurey

The following theorem of Maurey will be proved: Let $C$ be a 
weakly compact convex subset of a super-reflexive Banach space 
$X$, and let $T: C\rightarrow C$ be an isometry, i.e. 
$||Tx-Ty||=||x-y||$ for all $x,y\in C$. Then $T$ has a fixed point.
I will try to make the lecture as self contained as possible 
by reminding the audience all the necessary terms.


April 1, 2004
Emanuel Milman, 
Sections of Star-Bodies, the Fourier Transform, and the 
Busemann-Petty Problem (following Alexander Koldobsky).

We will show how to use the Fourier Transform as a powerful tool for
investigating the volumes of (n-1) dimensional sections of star-bodies in
R^n. Examples will include Minkowski's Theorem on the uniqueness of a
star-body with given volumes of sections, and generalizations of Meyer and
Pajor's results on the extremal sections of l_p balls. Our main aim will
be to give an analytic solution to the Busemann-Petty problem: Given two
symmetric convex bodies K,L in R^n, such that the volume of every (n-1)
dimensional section of K is less than the corresponding one for L, does it
follow that the volume of K is less than that of L? (Spoiler: the answer
is positive for n<=4, and negative for n>=5).


April 15, 2004
Limor Ben-Efraim, Will speak on the localization lemma of Kannan, Lovasz
and Simonovits and a sharp isoperimetric inequality for convex sets (after
R. Montenegro).


April 22, 2004
Gideon Schechtman, Some observations regarding Dvoretzky's theorem.

If X is an n-dimensional normed space and $\epsilon>0$ then X admits a
$c(\epsilon)\sqrt{\log n}$  dimensional subspace which is $1+\epsilon$ -
euclidean.  $c(\epsilon)$ is of order $\epsilon/(\log 1/\epsilon)^2$.
This is an improvement over the previously known $c(\epsilon)=\epsilon^2$.
The proof is quite simple modulo known results.
Time permitting, I'll also speak on a joint generalization of (Milman's
version of)
Dvoretsky's theorem and the Johnson-Lindenstaruss lemma.


May 13, 2004 
Limor Ben-Efraim, The localization lemma of Kannan, Lovasz 
and Simonovits. 



May 20, 2004
Assaf Naor,
Impossibility of dimension reduction in l_1.


June 10, 2004
Limor Ben-Efraim, The localization lemma of Kannan, Lovasz 
and Simonovits, Take 2.