Thursday, 31st March 2005, 4:00 pm

Mathematics Building, Lecture Hall 2

Assaf Naor

(Microsoft Research)

"The Lipschitz Extension Problem"

** Abstract: **

The Lipschitz extension problem asks for conditions on a pair
of metric spaces *X*, *Y* such that every *Y*-valued
Lipschitz map on a subset
of *X* can be extended to all of *X* with only a bounded
multiplicative loss
in the Lipschitz constant. This problem dates back to the work of
Kirszbraun and Whitney in the 1930s, and has been extensively
investigated in the past two decades. The methods used in this direction
are based on geometric, analytic and probabilistic arguments. In
particular, the methods involve stable processes, random projections,
random partitions of unity and the analysis of Markov chains in metric
spaces. In this talk we will present the main known results on the
Lipschitz extension problem, as well as several recent breakthroughs.

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

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