Mathematical Sciences: Analysis and Geometry on Nilpotent Lie Groups

本项目是由本科院校研究奖资助的数学研究项目。主题是李群，它与数学的许多领域相关，因为它们在体现各种系统的对称性方面的作用，无论是物理的，几何的还是代数的。更具体地说，Ratcliff教授和Benson教授将研究幂零李群的分析和微分几何。他们希望对由紧群作用于幂零李群而产生的Gelfand对进行分类。拉特克利夫教授计划对海森堡群的分布空间和算子进行离散分解。Benson教授计划探索零流形上的辛结构和溶剂流形上的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.