Mathematical Sciences: Real Algebraic Varieties

Kucharz DMS 95-03138该奖项支持W.Kucharz教授致力于实代数几何的研究。特别是，他将研究实代数簇上的实代数态射和向量丛。将特别强调使用交集理论和K-理论中的技术来显式计算不变量的方法。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。

Kucharz DMS 95-03138 This award supports the research of Professors W. Kucharz to work in real algebraic geometry. In particular he will study real algebraic morphisms and vector bundles on real algebraic varieties. There will be particular emphasis on methods to explicitly calculate invariants using techniques from intersection theory and K-theory. 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 algebpa, 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.