Mathematical Sciences: RUI: Geometric Tomography

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The principal investigator will study problems in geometric tomography and develop methods to reconstruct the geometry of convex bodies from projections. In particular he will explore new directions in the algorithmic aspects of reconstructing convex bodies and polytopes from X-rays, their interactive determination from X-rays, and the classification of intersection bodies. Two undergraduate students will work on parts of the project under the direction of the principal investigator. This award will support research in the general area of integral geometry. The geometry of a set may often be analyzed and described by a decomposition of the set into slices. The geometry of the slices is often fairly simple and easy to describe. The main difficulty in the analysis is usually the reconstruction of the underlying geometric features of the entire set from the geometry of the slices. One well know application of this area of mathematics is the CAT scan.