Thursday, 5th November 2009, 4:00 pm

Mathematics Building, Lecture Hall 2

Mikhail Katz

(Bar-Ilan University)

"Bi-Lipschitz approximation by finite-dimensional imbeddings"

** Abstract: **

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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