Equidistribution problems and semisimple Lie groups

等分布问题和半单李群研究者，在与W。t. Gan和A. Eskin利用调和分析和遍历理论的方法来理解不变多项式的整数表示的等分布现象。 研究者建议继续研究半单李群的齐次空间上的等分布问题，特别是与数论和几何有关的问题。例如，黎曼对称空间中的紧极大平坦问题或李群的各种齐性空间中的格的轨道问题是人们感兴趣的，遍历理论和半单李群的表示理论在数论中的应用是现代数学中新发现的工具之一。这些方法，在适用时，结果是非常强大的，解决了一些重要的问题，纯数论方法不能处理。该机构对这个交叉点上的问题很感兴趣，并希望开发出进一步的工具来处理这些问题。

Title: Equidistribution problems and semisimple Lie groupsThe investigator, in several joint works with W. T. Gan andA. Eskin, has exploited methods from harmonic analysis andergodic theory to understand the equidistribution phenomenon of integer representations of invariant polynomials. The investigator proposes to continue herstudy on equidistribution questions on homogeneous spacesof semisimple Lie groups, especially those connected with problems in number theory and geometry. For example, the problem of understanding compact maximal flats in Riemannian symmetric space or orbits of lattices in various homogeneous spaces of Lie groups are of interest.The application of ergodic theory and the representation theory of semisimple Lie groups in number theory is one of newly discoveredtools in modern mathematics. The methods, when applicable, turnout to be very powerful and solve some of the important problems whichpure number theoretic methods cannot deal with. The investigatoris interested in the problems at this intersection andhopes to develop further tools to deal with them.