Mathematical Sciences: Analysis and Geometry on Nilpotent Lie Groups

该项目是一项数学研究， 本科院校研究奖。 的主题 是李群，它与数学的许多领域都相关 因为它们在体现各种对称性方面的作用， 系统，无论是物理的，几何的，还是代数的。 更具体地说，拉特克利夫教授和本森教授将工作 关于幂零李群的分析和微分几何。 他们希望对由动作产生的盖尔芬德对进行分类 幂零李群上的紧群。 拉特克利夫教授 计划开发一个离散分解的分布空间 和海森堡群上的算子。 本森教授是 计划探索nil流形上的辛结构， 解流形上的Kaehler结构

This project is mathematical research funded under a Research in Undergraduate Institutions award. The subject matter is Lie groups, which are relevant to many areas of mathematics because of their role in embodying the symmetries of various systems, be they physical, geometrical, or algebraic. More specifically, Professors Ratcliff and Benson will work on analysis and differential geometry of nilpotent Lie groups. They hope to classify the Gelfand pairs that arise from actions of compact groups on nilpotent Lie groups. Professor Ratcliff plans to develop a discrete decomposition of distribution spaces and operators on the Heisenberg group. Professor Benson is planning to explore symplectic structures on nilmanifolds and Kaehler structures on solvmanifolds.