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WINTER MIDWEST TOPOLOGY SEMINAR

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Calvin College, Grand Rapids, Michigan

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February 26 and 27, 2005

** Speaker:** Gunnar Carlsson
** Title:** Algebraic topology and the qualitative analysis of point cloud data

** Time:** Canceled

** Abstract:** Algebraic topology allows one to
make precise various kinds of qualitative information ("connectivity information") about geometric objects. This kind of information can be quite useful in attempting to
understand the overall structure of the space in question. The methods have
mostly been restricted to situations in which one has complete information
about the spaces, and have typically only been evaluated by hand. In recent
years, however, methods have been developed which allow one to infer
connectivity information about a geometric object even though one may only
be given a finite (but large) set of points (called a point cloud) sampled
from it. We will discuss these developments, and illustrate the techniques
with an example from natural image statistics.

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