Departmental Colloquium
Alex Iosevich
University of Missouri at Columbia
Geometric configurations in Euclidean and discrete settings.
Abstract: We shall explore several different manifestations of the following general principle which says that if a subset of a vector space is large, in a suitable sense, than it contains a rigid copy of every finite geometric configuration. In the continuous setting, the size is typically measured using the Hausdorff dimension. In the discrete setting, the cardinality of the set plays this role. In vector spaces over finite fields, a combination of the two phenomena comes into play. An interplay of combinatorial, number theoretic and Fourier analytic methods is involved and the relationship between the different manifestations of the configuration problems will be emphasized throughout.
Friday February 20, 2009 at 3:00 PM in SEO 636