Gideon Schechtman
The William Petschek Professor of Mathematics
My major area of expertise is geometry
of normed spaces. We study properties of high dimensional convex sets (these
are sets of points in high dimensional space with the property that for any
two points in the set, the whole segment joining them is also in the set) and
other "nice" sets. The results are usually counter intuitive showing that high
dimensional spaces are very different from the three dimensional space some
of us think we live in. Another area I am interested in is classical probability
theory. Here we study fine behavior of random variables. The initial motivation
for this study is to use it as a tool in studying convex sets. (Typically one
shows that objects with a certain property exist by showing that "most" of the
relevant objects have this property, usually without being able to point at
even one explicit object possessing the desired property.) This study also leads
towards discoveries of limits laws, explaining why seemingly random quantities
in nature behave in quite a structured way.
Recent Publications
- [with W.B. Johnson, J. Lindenstrauss and D. Preiss] Lipschitz quotients from metric trees and from Banach spaces containing l1. J. Funct. Anal. 194 (2002) 332-346.
- [with W.B. Johnson] Very tight embeddings of subspaces of Lp, 1< p< 2, into lpn. Geometric and Funct. Anal. 13 (2003) 845-851.
- Special orthogonal splittings of L12k. Israel J., to appear.