Mathematical Sciences: Vector Bundles and Projective Geometry

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This award supports the research in Algebraic Geometry of Professor Lawrence Ein of the University of Illinois at Chicago. Dr. Ein has several projects, all concerned with the relation between vector bundles and projective geometry. Among these projects are the study of special Cremona transformations, dual varieties and syzygies of the generic canonical curve. This is research in the field of Algebraic Geometry, one of the oldest parts of modern mathematics, but one which has had a revolutionary flowering in the past quarter-century. In its origin, it treated figures that could be defined in the plane by the simplest equations, namely polynomials. Nowadays the field makes use of methods not only from Algebra, but from Analysis and Topology, and conversely is finding application in those fields as well as in theoretical Computer Science and in Robotics.