Mathematical Sciences: Intersection Theory, Mirror Symmetry and Computer Algebra

9311386 Katz这项资助支持S. Katz教授在代数几何方面的研究工作。他将研究由超弦理论产生的镜像对称猜想。他还将继续开发一个计算机代数包来进行交叉计算。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，它已经发展到解决了几个世纪以来一直存在的问题的程度。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，该领域不仅使用代数的方法，而且还使用分析和拓扑的方法，相反，它在这些领域中被广泛使用。此外，它已被证明在物理学、理论计算机科学、密码学、编码理论和机器人等多种领域都很有用。＊＊＊

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. ***