Mathematical Sciences: Studies in Algebraic Geometry

该奖项支持首席研究员I. Dolgachev教授和博士后助理V. Lunts博士在代数几何领域的研究。Dolgachev教授将研究曲线在射影空间中的Scorza不变量，以及某些超几何函数与模空间之间的联系。Lunts博士将研究旗变体上的Verma模的特征变体、硬Lefschetz定理和环变体的上同调。这项研究属于代数几何领域，是现代数学中最古老的部分之一，但在过去10年里，它发展到解决了几个世纪以来一直存在的问题的程度。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，该领域不仅使用代数的方法，而且还使用分析和拓扑的方法，相反，它在这些领域中被广泛使用。此外，它已被证明在物理学、理论计算机科学、密码学、编码理论和机器人等多种领域都很有用。

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.