Mathematical Sciences: The Algebro-Geometric Theory of Difference Equations

该奖项支持D. Gieseker教授在代数几何方面的研究。Gieseker教授将研究差分算子的等谱变形理论和代数曲面上的稳定束理论。他打算研究Toda格和稳定束模空间的不可约性。这项研究属于代数几何领域，是现代数学中最古老的部分之一，但在过去10年里，它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。

This awards supports the research of Professor D. Gieseker to work in algebraic geometry. Professor Gieseker will study the theory of isospectral deformations of difference operators and the theory of stable bundles on an algebraic surface. He intends to study the Toda lattice and the irreducibility of the moduli space of stable bundles. 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.