Mathematical Sciences: Curves on Special Surfaces and The Local Miyaoka-Yau Inequality

该奖项支持J.Wahl教授致力于代数几何的研究。Wahl教授将解决的问题之一将是研究K3曲面上的高斯映射，或者更一般地，研究具有平凡正则丛的可能奇异曲面上的高斯映射。他还将继续研究局部奇点的拓扑性质。这项研究使用了代数几何的技术，这是现代数学中最古老的部分之一，但在过去的25年里取得了革命性的成就。在它的起源中，它处理的是可以在平面上用最简单的方程定义的图形，即多项式。如今，该领域不仅使用代数的方法，而且使用分析和拓扑学的方法，反过来，在这些领域以及物理、理论计算机科学和机器人中也找到了应用。

This award supports the research of Professor J. Wahl to work in algebraic geometry. One of the problems that Professor Wahl will address will be studying Gaussian maps on K3 surfaces or more generally on possibly singular surfaces with trivial canonical bundle. He will also continue to study topological properties of local singularities. This research uses the techniques 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 physics, theoretical computer science, and robotics.