Mathematical Sciences: Moduli of Vector Bundles on AlgebraicSurfaces

该奖项支持J. Li教授的研究工作 在代数几何中。 他将研究向量的模空间 代数曲面上的丛他将特别研究 科代拉维数，Picard群，唐纳森多项式 不变量以及高阶丛的模空间。 这项研究是在代数几何领域，其中之一， 现代数学中最古老的部分，但其中一个蓬勃发展， 在过去的10年里，它解决了一些问题， 屹立了几个世纪最初，它处理的是 平面由最简单的方程，即多项式。今天 field不仅使用代数方法，还使用分析方法 和拓扑学，相反，它被广泛用于那些 领域的 此外，它已证明自己在不同领域的有用性， as physics物理，theoretical理论computer计算机science科学，cryptography密码学，coding编码 理论与机器人

This awards supports the research of Professor J. Li to work in algebraic geometry. He will study moduli spaces of vector bundles on algebraic surfaces. In particular he will study the Kodaira dimension, the Picard group, the Donaldson polynomial invariants as well as moduli spaces for higher rank bundles. 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.