Euler Systems and Their Applications

9401321这个奖项资助了维克多·科利维辛教授的研究。科利维金教授致力于欧拉系统理论及其在数论中的应用。对于给定的欧拉系统，他计划扩展局部显式控制的上同调类集合，并将它们与数域和椭圆曲线的运算联系起来。这项研究属于数论的总称。数论是研究全体数的性质的学科，是数学中最古老的分支。从一开始，数论中的问题就提供了创造新数学的动力，几乎在该学科的所有部分。科利维文教授在使用几何思想研究整数方面是一位领先者。这种数论是非常技术性和深刻性的，但它在理论计算机科学和编码理论等领域有着惊人的应用。

9401321 Kolyvagin This award funds the research of Prof. Victor Kolyvagin. Prof. Kolyvagin works on the theory of Euler systems and their application to number theory. For a given Euler system, he plans to extend the set of cohomology classes explicitly controlled locally, and connect them to the arithmetic of number fields and elliptic curves. This research falls under the general heading of number theory. Number theory is the study of the properties of the whole numbers and is the oldest branch of mathematics. From the beginning problems in number theory have furnished the driving force to creation of new mathematics in almost all parts of the discipline. Prof. Kolyvagin is a leader in the use of geometric ideas to study whole numbers. This kind of number theory is very technical and deep, but it has had astonishing applications in areas like theoretical computer science and coding theory.