This awards supports the research of Professors C. Delzell and J. Madden to work in real algebraic geometry. They will work on a general theory of local real algebraic geometry connecting singularities with intersections using notions from ordered fields. They also intend to work on relations between lattice ordered rings and real algebraic geometry, Lipschitz continuity and differentiability of abstract semialgebraic functions and smoothly varying solutions to Hilbert's 17'th problem. The 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.
