Counting and Equidistribution on homogeneous spaces

齐次空间上的计数和均匀分布

• 批准号: 0629322
• 负责人: Hee Oh
• 金额: $ 30.95万
• 依托单位: Brown University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-07-01 至 2012-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0629322&HistoricalAwards=false
• 关键词: Counting; Equidistribution; homogeneous; spaces

DMS-0629322Hee OhThe proposal concerns four projects regarding the distribution of geometric and arithmetic objects on homogeneous spaces of Lie groups. They are equidistribution of Hecke correspondence, counting rational points of bounded height, distribution of rational points with given denominator and distribution of values of irrational forms. They propose to use techniques from various different fields such as harmonic analysis, dynamics of group actions, ergodic theory, automorphic forms of semisimple algebraic groups in order to prove (or disprove) the equidistribution of densely distributed objects arising in number theoretic and geometric situation.One of big achievements in modern mathematics is the use of ergodic theory, dynamics of homogeneous spaces, arithmetic geometry and automorphic forms in solving long standing open problems in number theory. The proposed projects are focused on establishing further these connections between different disciplines of mathematics.

DMS-0629322 Hee Oh该提案涉及四个关于李群齐性空间上几何和算术对象分布的项目。它们是Hecke对应的等分布、有界高有理点的计数、给定分母有理点的分布和无理形式值的分布。他们建议使用各种不同领域的技术，如调和分析，群体作用动力学，遍历理论，半单代数群的自守形式，以证明（或反驳）数论和几何中出现的密集分布物体的等分布。现代数学的一个重大成就是遍历理论的应用，齐次空间的动力学，算术几何和自守形式在解决长期存在的开放问题的数论。拟议的项目的重点是建立进一步这些不同学科之间的数学联系。