Mathematical Sciences: Analytic Number Theory, Automorphic Forms, and Application

数学科学：解析数论、自同构形式及应用

• 批准号: 8912742
• 负责人: Carlos Moreno
• 金额: $ 3.37万
• 依托单位: CUNY Baruch College
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-11-01 至 1993-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8912742&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Analytic; Number; Theory

This award supports the research in algebraic geometry, coding theory, and analytic number theory of Professor Carlos J. Moreno of Baruch College of the City University of New York. Dr. Moreno will be working on several questions, all inter- disciplinary within mathematics. One of these is to apply techniques of algebraic geometry to the theory of the error correcting codes arising from algebraic curves that were first developed by Goppa. Another field in which Dr. Moreno will be working involves congruence properties for the weight multiplicities and partition functions of highest weight representations of Kac-Moody Lie algebras. The several themes of Professor Moreno's research are unified by his expertise in algebraic geometry. This is one of the oldest parts of modern mathematics, but one which has had a revolutionary flowering in the past quarter-century. In its origin, it treated figures that could be defined in the plane by the simplest equations, namely polynomials. Nowadays the field makes use of methods not only from algebra, but from analysis and topology, and conversely is finding application in those fields as well as in theoretical computer science and in robotics.

该奖项支持纽约城市大学巴鲁克学院的Carlos J. Moreno教授在代数几何、编码理论和解析数论方面的研究。莫雷诺博士将研究几个问题，这些问题都是数学领域的跨学科问题。其中之一是将代数几何技术应用于由Goppa首先提出的代数曲线产生的纠错码理论。莫雷诺博士将研究的另一个领域涉及Kac-Moody李代数的权重多重和最高权重表示的配分函数的同余性质。莫雷诺教授研究的几个主题是由他在代数几何方面的专业知识统一的。这是现代数学中最古老的部分之一，但在过去的四分之一个世纪里，它已经有了革命性的发展。在它的起源中，它处理的图形可以用最简单的方程，即多项式，在平面上定义。如今，该领域不仅利用代数的方法，而且利用分析和拓扑的方法，反过来，在这些领域以及理论计算机科学和机器人技术中也得到了应用。