9401509 Delzell This awards supports the research of Professors C. Delzell and J. Madden to work in real algebraic geometry. In particular they will try to extend their theory of local real algebraic geometry from dimension two to dimension 3. They will also study consequences of their recent proof of the existence of a completely normal spectral space which is not the real spectrum of any commutative ring. This research is in the field of algebraic geometry, one of the oldest parts of modern mathematics, but one which blossomed to the point where it has, in the past 10 years, solved problems that have stood for centuries. Originally, it treated figures defined in the plane by the simplest of equations, namely polynomials. Today, the field uses methods not only from algebra, but also from analysis and topology, and conversely it is extensively used in those fields. Moreover it has proved itself useful in fields as diverse as physics, theoretical computer science, cryptography, coding theory and robotics.
