Jerusalem Mathematics Colloquium

Thursday, 5th November 2009, 4:00 pm
Mathematics Building, Lecture Hall 2

Mikhail Katz
(Bar-Ilan University)

"Bi-Lipschitz approximation by finite-dimensional imbeddings"


Gromov's celebrated systolic inequality from '83 is a universal volume lower bound for an essential manifold M in terms of the least length of a noncontractible loop in M. His proof passes via a strongly isometric imbedding called the Kuratowski imbedding, into the Banach space of bounded functions on M. We show that the imbedding admits an approximation by a (1+C)-bi-Lipschitz (onto its image), finite-dimensional imbedding for every C>0. Our key tool is the first variation formula thought of as a real statement in first-order logic, in the context of non-standard analysis.

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

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