Mathematical Sciences: Iwasawa Theory for p-adic representations

格林伯格教授将继续研究塞尔默群的性质及其与数论和代数几何中自然出现的某些l函数值的联系。三个看似独立的现代数学领域在这个项目中相遇：数论、代数几何和分析。数论意味着研究整数，静态的和离散的；代数几何开始于研究线和平面等结构的关系和运动，但近年来呈现出越来越抽象和代数的基调；分析指的是与微积分相关的广阔的数学领域。现代算术代数几何从这三个领域汲取知识，同时又对它们作出贡献，这是当今数学中最令人兴奋的发展之一。

Professor Greenberg will continue his investigations of the properties of Selmer groups and their connections with values of certain L-functions that occur naturally in number theory and algebraic geometry. Three seemingly separate fields of modern mathematics meet in this project: Number Theory, Algebraic Geometry, and Analysis. Number Theory means the study of the whole numbers, static and discrete; Algebraic Geometry began with the study of the relations and motions of constructs like lines and planes, but has taken on an ever more abstract and algebraic tone in recent years; Analysis refers to that broad region of mathematics that is related to Calculus. That modern arithmetical algebraic geometry is drawing from these three fields and simultaneously making contributions to them is one of the most exciting developments in mathematics today.