# Jerusalem Mathematics Colloquium

Thursday, 16th November 2006, 4:00 pm

Mathematics Building, Lecture Hall 2

##

Shiri Artstein

(Tel Aviv University)

"Coverings and Metric Entropy: Duality"

** Abstract: **

A well known 30 year old conjecture in the field of Asymptotic
Geometric Analysis is the duality of entropy numbers conjecture,
which concerns the quantifying, in terms of covering numbers, of the
classical fact that if a linear operator between two Banach Spaces
is compact then so is its dual. The most important case (which is the one
appearing in applications to probability theory, ergodic theory, learning
theory and other fields) is when one of the two spaces is a Hilbert
space.
In 2003, jointly with V.D. Milman and S.J. Szarek, we proved the duality
conjecture in this case. More recently, in a joint work together also
with N. Tomczak-Jaegermann, we generalized this theorem to a wide class
of spaces (which include for example all uniformly convex and all
uniformly smooth spaces). This generalization invloved a new notion of
'convexified packing' which is of independent interest.

In the talk I will discuss these notions and results, and present, as much
as time permits, the main ideas of the proofs.

Light refreshments will be served in the faculty lounge at 3:30.

List of talks, 2006-07

Archive of talks