Gideon Schechtman

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MAX CUT is the problem of partitioning the vertices of a graph into two sets max imizing the number of edges joining these sets This problem is NP hard Goemans and Williamson proposed an algorithm that rst uses a semide nite programming relaxation of MAX CUT to embed the vertices of the graph on the surface of an n dimensional sphere and then uses a random(More)
New concepts related to approximating a Lipschitz function between Banach spaces by a ne functions are introduced Results which clarify when such approximations are possible are proved and in some cases a complete characterization of the spaces X Y for which any Lipschitz function from X to Y can be so approx imated is obtained This is applied to the study(More)
What is complexity, and how should it be studied mathematically? In the interpretation that we adopt, there are several underlying common themes to complexity theories. The basic ground rules are these: There is a family F of some mathematical objects under consideration. The elements of some subset S ⊆F are deemed simple. Also, there are certain(More)
We show that any L<sub>1</sub> embedding of the transportation cost (a.k.a. Earthmover) metric on probability measures supported on the grid {0,1,..., n}<sup>2</sup> sube Ropf<sup>2</sup> incurs distortion Omega(radic;(log n)). We also use Fourier analytic techniques to construct a simple L<sub>1</sub> embedding of this space which has distortion O(log n)
Concentration inequalities are estimates for the degree of approximation of functions on metric probability spaces around their mean. It turns out that in many natural situations one can give very good such estimates, and that these are extremely useful. We survey here some of the main methods for proving such inequalities and give a few examples to the way(More)
The main result is that a Banach space X is not super-reflexive if and only if the diamond graphs Dn Lipschitz embed into X with distortions independent of n. One of the consequences of that and previously known results is that dimension reduction a-la Johnson–Lindenstrauss fails in any non super reflexive space with non trivial type. We also introduce the(More)
We give several sufficient conditions on a pair of Banach spaces X and Y under which each Lipschitz mapping from a domain in X to Y has, for every ǫ > 0, a point of ǫ-Fréchet differentiability. Most of these conditions are stated in terms of the moduli of asymptotic smoothness and convexity, notions which appeared in the literature under a variety of names.(More)