Mathematical Sciences: Stable Bundles on Algebraic Surfaces

该奖项支持D. Gieseker教授在代数几何方面的研究。他将研究代数表面上的稳定束和差分算子的等谱变形理论，特别是Toda晶格的二维版本。他还将研究一种计算唐纳森多项式的可能方法。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。

This awards supports the research of Professor D. Gieseker to work in algebraic geometry. He will study stable bundles on algebraic surfaces and the theory of isospectral deformations of difference operators, in particular a two dimensional version of the Toda lattice will be studied. He will also investigate a possible method for computing Donaldson polynomials. 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.