Abstract:

In the last several years a number of very interesting
results were proved about finite metric spaces. Some of this work is
motivated by practical considerations: Large data sets (coming e.g. from
computational molecular biology, brain research or data mining) can be
viewed as large metric spaces that should be analyzed (e.g. correctly
clustered). On the other hand, these investigations connect to some
classical areas of geometry - the asymptotic theory of finite-dimensional 
normed spaces and differential geometry. Finally, the metric theory 
of finite graphs has proved very useful in the study of
graphs per se and the design of approximation algorithms for hard
computational problems. In this talk I will try to explain some of the
results and review some of the emerging new connections and the many
fascinating open problems in this area.