Mathematical Sciences: Topics in Real Algebraic Geometry

该奖项支持C.Delzell教授和J.Madden教授在真实代数几何领域的研究。他们将致力于局部实代数几何的一般理论，使用有序域中的概念将奇点与交集联系起来。他们还打算研究格序环和实代数几何之间的关系，抽象半代数函数的Lipschitz连续性和可微性，以及Hilbert第17‘问题的光滑变化解。这项研究是在代数几何领域进行的，代数几何是现代数学中最古老的部分之一，但在过去的10年里，它发展到了解决了几个世纪以来的问题的地步。最初，它用最简单的方程，即多项式来处理平面上定义的图形。今天，这个领域不仅使用代数的方法，而且还使用分析和拓扑学的方法，相反，它在这些领域被广泛使用。此外，它在物理、理论计算机科学、密码学、编码理论和机器人学等领域都证明了自己的有用。

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.