Mathematical Sciences: Studies in Algebraic Geometry

该奖项支持I教授的研究。多尔加切夫 作为首席研究员，V. Lunts博士作为博士后 在代数几何方面工作。 多尔加切夫教授 将研究射影空间中曲线的Scorza不变量， 以及某些超几何函数之间的联系 和模空间 伦茨博士将研究 Verma模在旗变种上的变种，硬Lefschetz 定理和复曲面簇的上同调。 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 在过去的10年里， 已经屹立了几个世纪 最初，它把数字 在平面上由最简单的方程定义，即 多项式 今天，该领域使用的方法不仅来自 代数，但也从分析和拓扑学，反过来说，它 广泛应用于这些领域。 此外，它还证明， 它本身在物理学、理论、 计算机科学、密码学、编码理论和机器人技术。

This awards supports the research of Professor I. Dolgachev as principal investigator and Dr. V. Lunts as a postdoctoral associate to work in algebraic geometry. Professor Dolgachev will study the Scorza invariant of curves in projective space, as well as the connection between certain hypergeometric functions and moduli spaces. Dr. Lunts will work on characteristic varieties of Verma modules on flag varieties, the hard Lefschetz theorem and the cohomology of toric varieties. 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.