16:30
A map betweem metric spaces is a bilipschitz homeomorphism if it
is Lipschitz and has a Lipschitz inverse; a map is a bilipschitz embedding
if it is a bilipschitz homeomorphism onto its image. Given metric spaces
X and Y, one may ask if there is a bilipschitz embedding X--->Y, and if
so, one may try to find an embedding with minimal distortion, or at least
estimate the best bilipschitz constant. Such bilipschitz embedding
problems arise in various areas of mathematics, including geometric group
theory, Banach space geometry, and geometric analysis; in the last 10
years they have also attracted a lot of attention in theoretical computer
science.
The lecture will be a survey bilipschitz embedding in Banach spaces from
the viewpoint of geometric analysis.