Mathematical Sciences: Research in Algebra and Algebraic Number Theory

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This research is concerned with problems in algebraic geometry. The principal investigator will continue his study of motivic cohomology and establishing connections with algebraic K-theory and the values of Dedekind zeta functions. There are possible applications to the Soule-Beilinson conjecture and related topics which will also be explored. 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 origins, 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 robotics.