DIFFERENTIAL GEOMETRY SEMINAR

                              Monday, May 22

                            Communications 226
                                 3:45 p.m.


                                Brent Smith
                        (University of Washington)

                        THE GROMOV-HAUSDORFF METRIC


In this talk I will discuss a tool developed by M. Gromov for the study of
global Riemannian geometry. Put simply, his idea is to introduce a metric
space structure on the collection of Riemannian manifolds. This allows one
to ask questions about the topology of this collection and its subsets and
to consider limits of sequences of manifolds. The distance function we will
consider is the Gromov-Hausdorff distance which is a direct generalization
of the classical Hausdorff distance between subsets of a metric space. As a
nice illustration of the ideas involved, I will present the proof of
Gromov's Precompactness Theorem which states that any collection of compact
n-dimensional Riemannian manifolds with a lower bound on Ricci curvature
and an upper bound on diameters is precompact as a subset of the collection
of all compact metric spaces. A number of applications will then be
presented.

This talk has the unique feature that it will be accessible even to those
who have not yet taken the Geometric Structures sequence.


For more information about this seminar, view the Differential Geometry
Seminar World-Wide Web page at 

    https://www.math.washington.edu/~lee/Seminars/dg.html


To request disability accommodations, contact the Office of the ADA
Coordinator, at least ten days in advance of the event: 543-6450 (voice);
543-6452 (TDD); 685-3885 (FAX); access@u.washington.edu (E-mail).