Mathematical Sciences: Anti Self-dual Connections on Algebraic Surfaces

该奖项支持加州大学洛杉矶分校的David Gieseker教授在代数几何方面的研究。Gieseker博士的研究将是差分算符的等谱理论，考虑二维周期差分算符的Bloch流形的Picard群。他还将探索布洛赫流形构造在其他情况下的推广，如任意属曲面的三角化。这是代数几何领域的研究，代数几何是现代数学中最古老的部分之一，但在过去的四分之一个世纪里，它已经有了革命性的发展。在它的起源中，它处理的图形可以用最简单的方程，即多项式，在平面上定义。如今，该领域不仅使用代数的方法，还使用分析和拓扑的方法，相反，在这些领域以及理论计算机科学，机器人技术和物理学中也得到了应用。

This award supports the research in Algebraic Geometry of Professor David Gieseker of the University of California at Los Angeles. Dr. Gieseker's investigations will be in the isospectral theory of difference operators, considering the Picard group of the Bloch manifold of a two-dimensional periodic difference operator. He will also explore generalizations of the Bloch manifold construction to other contexts such as the triangular- ization of a surface of arbitrary genus. This is research in the field of Algebraic Geometry, one of the oldest parts of modern mathematics, but one which has had a revolutionary flowering in the past quarter-century. In its origin, it treated figures that could be defined in the plane by the simplest equations, namely polynomials. Nowadays the field makes use of methods not only from Algebra, but from Analysis and Topology, and conversely is finding application in those fields as well as in theoretical Computer Science, Robotics, and Physics.