Mathematical Sciences: Studies in Algebraic Geometry

该奖项支持I.Dolgachev教授作为首席研究员和V.LUNTS博士作为博士后助理从事代数几何工作的研究。Dolgachev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与模空间之间的联系。伦茨博士将研究FLAG簇上的Verma模的特征簇、Hard Lefschetz定理和Toric簇的上同调。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，它发展到了解决了几个世纪以来的问题的地步。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，这个领域不仅使用代数的方法，而且还使用分析和拓扑学的方法，相反，它在这些领域被广泛使用。此外，它在物理、理论计算机科学、密码学、编码理论和机器人学等领域都证明了自己的有用。

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.