This award supports the research in algebraic geometry of Professors Henry Pinkham, Robert Friedman, and David Bayer of Columbia University. Drs. Pinkham and Bayer intend to mount a computational and theoretical attack on one of the most resistant problems of modern mathematics, the Jacobian Conjecture. Dr. Friedman's project involves an ongoing investigation into the structure of moduli spaces of stable vector bundles on an algebraic surface. Algebraic geometry is 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 physics, theoretical computer science, and robotics.
