Mathematical Sciences: Two Problems in Modular Surfaces

数学科学：模曲面中的两个问题

• 批准号: 9203397
• 负责人: Mark Sheingorn
• 金额: $ 3.06万
• 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: 1992
• 资助国家: 美国
• 起止时间: 1992-07-01 至 1994-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9203397&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Two; Problems; Modular

Professor Sheingorn will work on several problems connected with automorphic forms. In particular, he will study the consequences of the insight that certain number theoretic objects are equivalent to geometric traits of geodesics on highly symmetric spaces. Automorphic forms arose out of non-Euclidean geometry in the middle of the nineteenth century. Both mathematicians and physicists have thus long realized that many objects of fundamental importance are non-Euclidean in their basic nature. This field is principally concerned with questions about the whole numbers, but in its use of geometry and analysis, it retains connection to its historical roots and thus to problems in areas as diverse as gauge theory in theoretical physics and coding theory in information theory.

Sheingorn教授将致力于研究几个与 具有自守形式。 特别是，他将研究 某些数论对象 等价于测地线的几何特征， 对称空间 自守形式产生于非欧几里德几何， 世纪中期。 数学家和 物理学家早就意识到， 基本的重要性是非欧几里德在其基本性质。 此字段主要涉及有关 整数，但在其使用的几何和分析，它 保留了与其历史根源的联系，从而与问题 从理论物理中的规范理论， 信息论中的编码理论