Department Colloquium
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Speaker:
Kevin Knudson Department of Mathematics and Statistics Mississippi State University Time and Place: 3:30 p.m., Friday, February 10, 2006, 14 Allen Title: ALGORITHMS IN DISCRETE MORSE THEORY Abstract: Given a smooth real-valued map on a manifold, M, it is relatively easy to find its critical points, gradient flow, etc. But what if one has the values of a function at only a finite sample of points of M? Is it possible to find critical points and to construct a reasonable gradient flow? In the mid-90's, Forman introduced a version of Morse theory on cell complexes that is particularly well-suited to studying this problem. In this talk, I will present an algorithm for extending an arbitrary function f, defined on the vertices of a finite simplicial complex K (e.g. a triangulated manifold), to a discrete Morse function on K in such a way that the associated gradient flow mirrors the large-scale behavior of f. I will present several examples and applications ranging from terrain mapping to analysis of CT images. Refreshments: 3:00-3:30 p.m., 467 Allen |
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