Mathematical Sciences: Ergodic Theory, P-adic Lie Groups andNumber Theory

数学科学：遍历理论、P-进李群和数论

• 批准号: 9311589
• 负责人: Marina Ratner
• 金额: $ 19.63万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-06-01 至 1998-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9311589&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Ergodic; Theory; adic

Ratner's project will 10 extend Raghunathan's conjectures to p-adic Lie groups, 2) study the dynamical properties of the geodesics and the horocycle flows on homogeneous spaces of SL(2,Q_p), 3) apply previous results on orbit closures of unipotent flows to find asymptotic growth rate of integral solutions of quadratic inequalities, and 4) study Principal Congruence groups and the Ramanujan-Selberg Conjecture. This project involves research in ergodic theory. Ergodic theory in general concerns understanding the average behavior of systems whose dynamics is too complicated or chaotic to be followed in microscopic detail. Under the heading "dynamics can be placed the modern theory of how groups of abstract transformations act on smooth spaces. In this way ergodic theory makes contact with geometry in its quest to classify flows on homogeneous spaces.

Ratner 的项目将 10 将 Raghunathan 的猜想扩展到 p 进李群，2）研究 SL(2,Q_p) 齐次空间上测地线和四环流的动力学性质，3) 应用先前关于单能流轨道闭包的结果来找到二次不等式积分解的渐近增长率，4) 研究主同余群和 拉马努金-塞尔伯格猜想。 该项目涉及遍历理论的研究。 一般来说，遍历理论涉及理解系统的平均行为，这些系统的动力学过于复杂或混乱，无法在微观细节中遵循。 在“动力学”标题下，可以放置关于抽象变换组如何作用于平滑空间的现代理论。通过这种方式，遍历理论在寻求对同质空间上的流进行分类的过程中与几何学建立了联系。