Mathematical Sciences: Research in Algebraic Geometry

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Kleiman This supports the research of Professors S. Kleiman and M. Artin with Dr. J. Pommersheim as a post-doctoral associate. Kleiman will continue to work on Buchsbaum-Rim multiplicity and equi-singularity. Artin will continue to work on the foundations of non-commutative algebraic geometry. Pommersheim will work on the connection between toric varieties and number theory. This is research in the field of algebraic geometry broadly conceived. Algebraic geometry itself 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. ***