Mathematical Sciences: Infinite Dimensional Lie Groups

约书亚·莱斯利将继续他在无限维李群理论方面的研究。这是一个日益重要的领域，因为它的物理应用。主要目标是调查众所周知的有限维理论在多大程度上能够适应这种更困难的环境。Leslie将使用他最近建立的技术来尝试将李群与Kac-Moody李代数的某些完备化联系起来。这是一个困难的问题，但他的泛函分析方法已经被证明是成功的，当应用于许多重要的例子类别时。

Joshua Leslie will continue his research in the theory of infinite dimensional Lie groups. This is an area of growing importance because of its physical applications. The major objective is to investigate the extent to which the well known finite dimensional theory can be adapted to this more difficult setting. Leslie will use his recently established techniques to try to associate Lie groups to certain completions of Kac-Moody Lie algebras. This is a difficult problem but his functional analytic methods have already proved to be successful when applied to numerous significant classes of examples.