Discrete subgroups of Lie groups

本课题主要研究半单李群及其离散子群的结构、分类和描述。 我们正在研究与数论和几何有关的问题。 我们使用的技巧涉及代数群、算术群、齐次空间上流的动力学性质和无穷维酉表示等理论。半单李群及其格是几何或算术对象的特殊对称性集合。 这项研究的目的是促进对对称性的理解，对称性的研究已被证明是数学和物理学的中心主题之一。其中一些已经在计算机科学和量子力学等领域得到了显著的应用。

AbstractOhThe proposed project mainly deals with understanding of the structure, classification anddescription of semisimple Lie groups as well as their discrete subgroups. We are investigating problems arising in connection with number theory and geometry. The techniques we have used involve the theories of algebraic groups, arithmetic groups, dynamical properties of flows on homogeneous spaces and infinite dimensional unitary representations.A semisimple Lie group and its lattices are special collections of symmetries of a geometric or arithmetic object. This research aims to contribute to understanding of the symmetries whosestudy has proven to be one of the central themes in mathematics and physics. Some of these has found remarkable applications in such fields as computer science and quantum mechanics.