Mathematical Sciences: Topology of Complex Projective Curves and Surfaces

9307896 Hironaka本奖项支持E. Hironaka教授在代数几何方面的研究工作。要研究的主题包括复杂品种的几何，特别是光滑表面和嵌入曲线。她特别希望找到计算这些几何物体的贝蒂数的方法。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。＊＊＊

9307896 Hironaka This awards supports the research of Professor E. Hironaka to work in algebraic geometry. Topics to be studied include the geometry of complex varieties, especially smooth surfaces and embedded curves. In particular she hopes to find ways to compute Betti numbers for these geometric objects. 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. ***