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. More recently I am
involved also in applications of the two fields above to questions in
theoretical computer science.
Recent Publications
- Two observations regarding embedding subsets of Euclidean spaces in normed spaces. Advances in Mathematics 200 (2006) 125-135.
- [with W.B. Johnson and B. Maurey] Weakly null sequences in L1. J. Amer. Math. Soc. 20 (2007) no. 1, 25-36.
- [with A. Naor] Planar earthmover is not in L1. SIAM Journal on Computing, to appear.