Mathematical Sciences: Intersection Theory, Mirror Symmetry and Computer Algebra

9311386卡茨这笔赠款支持S·卡茨教授从事代数几何方面的研究。他将研究源自超弦理论的镜像对称猜想。他还将继续开发一个用于进行交叉点计算的计算机代数包。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。***

9311386 Katz This grant supports the research of Professor S. Katz to work in algebraic geometry. He will work on the mirror symmetry conjecture that arose from superstring theory. He will also continue to develop a computer algebra package for doing intersection computations. 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. ***