Mathematical Sciences: Topics in Real Algebraic Geometry

小行星9401509 该奖项支持C教授的研究。Delzell和J. Madden致力于真实的代数几何。特别是他们将试图扩大他们的理论，当地的真实的代数几何从二维到三维。他们还将研究后果，他们最近证明存在一个完全正常的频谱空间，这不是真实的频谱的任何交换环。 这项研究是在代数几何领域，这是现代数学最古老的部分之一，但在过去的10年里，它已经发展到解决了几个世纪以来的问题。最初，它处理由最简单的方程，即多项式在平面上定义的图形。今天，该领域使用的方法不仅来自代数，而且来自分析和拓扑学，相反，它被广泛用于这些领域。 此外，它已被证明在物理学、理论计算机科学、密码学、编码理论和机器人学等不同领域都很有用。

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.